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UIC / Mathematics / MATH 180 / Give an example of the properties of inx.

Give an example of the properties of inx.

Give an example of the properties of inx.

Description

School: University of Illinois at Chicago
Department: Mathematics
Course: Calculus I
Professor: Dale embers
Term: Fall 2016
Tags: Calculus
Cost: 25
Name: 3.9 Logarithms
Description: These notes are on logarithms and will be on the upcoming exam.
Uploaded: 10/09/2016
1 Pages 183 Views 0 Unlocks
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ol.lst-kix_gw16n5qq267j-0.start{counter-reset:lst-ctn-kix_gw16n5qq267j-0 0}ol.lst-kix_50pmlbck485l-6.start{counter-reset:lst-ctn-kix_50pmlbck485l-6 0}ol.lst-kix_4dcjlvssrtx3-3.start{counter-reset:lst-ctn-kix_4dcjlvssrtx3-3 0}ol.lst-kix_ul8kb4iuqop2-8.start{counter-reset:lst-ctn-kix_ul8kb4iuqop2-8 0}.lst-kix_gw16n5qq267j-8 > li{counter-increment:lst-ctn-kix_gw16n5qq267j-8}.lst-kix_ul8kb4iuqop2-7 > li{counter-increment:lst-ctn-kix_ul8kb4iuqop2-7}.lst-kix_4dcjlvssrtx3-2 > li{counter-increment:lst-ctn-kix_4dcjlvssrtx3-2}.lst-kix_byhv03d04cj2-6 > li{counter-increment:lst-ctn-kix_byhv03d04cj2-6}.lst-kix_gw16n5qq267j-6 > li{counter-increment:lst-ctn-kix_gw16n5qq267j-6}ol.lst-kix_82e1y4o5f3wq-2.start{counter-reset:lst-ctn-kix_82e1y4o5f3wq-2 0}.lst-kix_byhv03d04cj2-8 > li{counter-increment:lst-ctn-kix_byhv03d04cj2-8}.lst-kix_50pmlbck485l-0 > li:before{content:"" counter(lst-ctn-kix_50pmlbck485l-0,decimal) ". "}ol.lst-kix_gw16n5qq267j-6.start{counter-reset:lst-ctn-kix_gw16n5qq267j-6 0}.lst-kix_50pmlbck485l-1 > li:before{content:"" counter(lst-ctn-kix_50pmlbck485l-1,lower-latin) ". "}ol.lst-kix_ul8kb4iuqop2-0{list-style-type:none}ol.lst-kix_ul8kb4iuqop2-2{list-style-type:none}ol.lst-kix_byhv03d04cj2-0.start{counter-reset:lst-ctn-kix_byhv03d04cj2-0 0}ol.lst-kix_ul8kb4iuqop2-1{list-style-type:none}.lst-kix_50pmlbck485l-2 > li:before{content:"" counter(lst-ctn-kix_50pmlbck485l-2,lower-roman) ". "}.lst-kix_50pmlbck485l-4 > li:before{content:"" counter(lst-ctn-kix_50pmlbck485l-4,lower-latin) ". "}ol.lst-kix_ul8kb4iuqop2-4{list-style-type:none}.lst-kix_50pmlbck485l-3 > li{counter-increment:lst-ctn-kix_50pmlbck485l-3}ol.lst-kix_ul8kb4iuqop2-3{list-style-type:none}ol.lst-kix_ul8kb4iuqop2-6{list-style-type:none}ol.lst-kix_ul8kb4iuqop2-5{list-style-type:none}.lst-kix_50pmlbck485l-3 > li:before{content:"" counter(lst-ctn-kix_50pmlbck485l-3,decimal) ". "}.lst-kix_50pmlbck485l-7 > li:before{content:"" counter(lst-ctn-kix_50pmlbck485l-7,lower-latin) ". "}ol.lst-kix_ul8kb4iuqop2-8{list-style-type:none}ol.lst-kix_ul8kb4iuqop2-7{list-style-type:none}.lst-kix_50pmlbck485l-6 > li:before{content:"" counter(lst-ctn-kix_50pmlbck485l-6,decimal) ". "}.lst-kix_4dcjlvssrtx3-0 > li{counter-increment:lst-ctn-kix_4dcjlvssrtx3-0}ol.lst-kix_82e1y4o5f3wq-8.start{counter-reset:lst-ctn-kix_82e1y4o5f3wq-8 0}.lst-kix_50pmlbck485l-5 > li:before{content:"" counter(lst-ctn-kix_50pmlbck485l-5,lower-roman) ". "}.lst-kix_82e1y4o5f3wq-0 > li{counter-increment:lst-ctn-kix_82e1y4o5f3wq-0}ol.lst-kix_gw16n5qq267j-5.start{counter-reset:lst-ctn-kix_gw16n5qq267j-5 0}ol.lst-kix_ul8kb4iuqop2-3.start{counter-reset:lst-ctn-kix_ul8kb4iuqop2-3 0}ol.lst-kix_4dcjlvssrtx3-8.start{counter-reset:lst-ctn-kix_4dcjlvssrtx3-8 0}ol.lst-kix_4dcjlvssrtx3-2.start{counter-reset:lst-ctn-kix_4dcjlvssrtx3-2 0}ol.lst-kix_82e1y4o5f3wq-7.start{counter-reset:lst-ctn-kix_82e1y4o5f3wq-7 0}.lst-kix_gw16n5qq267j-4 > li{counter-increment:lst-ctn-kix_gw16n5qq267j-4}ol.lst-kix_50pmlbck485l-0.start{counter-reset:lst-ctn-kix_50pmlbck485l-0 0}.lst-kix_50pmlbck485l-5 > li{counter-increment:lst-ctn-kix_50pmlbck485l-5}.lst-kix_ul8kb4iuqop2-0 > li{counter-increment:lst-ctn-kix_ul8kb4iuqop2-0}.lst-kix_82e1y4o5f3wq-7 > li{counter-increment:lst-ctn-kix_82e1y4o5f3wq-7}ol.lst-kix_ul8kb4iuqop2-2.start{counter-reset:lst-ctn-kix_ul8kb4iuqop2-2 0}.lst-kix_82e1y4o5f3wq-4 > li{counter-increment:lst-ctn-kix_82e1y4o5f3wq-4}ol.lst-kix_50pmlbck485l-1.start{counter-reset:lst-ctn-kix_50pmlbck485l-1 0}ol.lst-kix_50pmlbck485l-7.start{counter-reset:lst-ctn-kix_50pmlbck485l-7 0}ol.lst-kix_byhv03d04cj2-1{list-style-type:none}ol.lst-kix_byhv03d04cj2-0{list-style-type:none}ol.lst-kix_byhv03d04cj2-3{list-style-type:none}ol.lst-kix_byhv03d04cj2-2{list-style-type:none}ol.lst-kix_byhv03d04cj2-5{list-style-type:none}ol.lst-kix_byhv03d04cj2-4{list-style-type:none}ol.lst-kix_byhv03d04cj2-7{list-style-type:none}ol.lst-kix_byhv03d04cj2-6{list-style-type:none}ol.lst-kix_byhv03d04cj2-8{list-style-type:none}.lst-kix_4dcjlvssrtx3-7 > li{counter-increment:lst-ctn-kix_4dcjlvssrtx3-7}.lst-kix_82e1y4o5f3wq-8 > li:before{content:"" counter(lst-ctn-kix_82e1y4o5f3wq-8,lower-roman) ". "}ol.lst-kix_byhv03d04cj2-1.start{counter-reset:lst-ctn-kix_byhv03d04cj2-1 0}ol.lst-kix_gw16n5qq267j-7.start{counter-reset:lst-ctn-kix_gw16n5qq267j-7 0}.lst-kix_82e1y4o5f3wq-0 > li:before{content:"" counter(lst-ctn-kix_82e1y4o5f3wq-0,decimal) ". "}ol.lst-kix_ul8kb4iuqop2-1.start{counter-reset:lst-ctn-kix_ul8kb4iuqop2-1 0}.lst-kix_4dcjlvssrtx3-8 > li{counter-increment:lst-ctn-kix_4dcjlvssrtx3-8}.lst-kix_ul8kb4iuqop2-3 > li{counter-increment:lst-ctn-kix_ul8kb4iuqop2-3}.lst-kix_gw16n5qq267j-0 > li{counter-increment:lst-ctn-kix_gw16n5qq267j-0}.lst-kix_ul8kb4iuqop2-0 > li:before{content:"" counter(lst-ctn-kix_ul8kb4iuqop2-0,decimal) ". "}.lst-kix_ul8kb4iuqop2-1 > li{counter-increment:lst-ctn-kix_ul8kb4iuqop2-1}ol.lst-kix_4dcjlvssrtx3-1.start{counter-reset:lst-ctn-kix_4dcjlvssrtx3-1 0}.lst-kix_4dcjlvssrtx3-6 > li{counter-increment:lst-ctn-kix_4dcjlvssrtx3-6}.lst-kix_82e1y4o5f3wq-3 > li{counter-increment:lst-ctn-kix_82e1y4o5f3wq-3}.lst-kix_byhv03d04cj2-7 > li:before{content:"" counter(lst-ctn-kix_byhv03d04cj2-7,lower-latin) ". "}.lst-kix_byhv03d04cj2-4 > li{counter-increment:lst-ctn-kix_byhv03d04cj2-4}.lst-kix_byhv03d04cj2-3 > li:before{content:"" counter(lst-ctn-kix_byhv03d04cj2-3,decimal) ". "}.lst-kix_gw16n5qq267j-5 > li{counter-increment:lst-ctn-kix_gw16n5qq267j-5}.lst-kix_ul8kb4iuqop2-6 > li:before{content:"" counter(lst-ctn-kix_ul8kb4iuqop2-6,decimal) ". "}.lst-kix_byhv03d04cj2-1 > li:before{content:"" counter(lst-ctn-kix_byhv03d04cj2-1,lower-latin) ". "}.lst-kix_ul8kb4iuqop2-4 > li:before{content:"" counter(lst-ctn-kix_ul8kb4iuqop2-4,lower-latin) ". "}.lst-kix_82e1y4o5f3wq-2 > li{counter-increment:lst-ctn-kix_82e1y4o5f3wq-2}.lst-kix_82e1y4o5f3wq-8 > li{counter-increment:lst-ctn-kix_82e1y4o5f3wq-8}.lst-kix_ul8kb4iuqop2-2 > li:before{content:"" counter(lst-ctn-kix_ul8kb4iuqop2-2,lower-roman) ". "}.lst-kix_50pmlbck485l-4 > li{counter-increment:lst-ctn-kix_50pmlbck485l-4}.lst-kix_82e1y4o5f3wq-2 > li:before{content:"" counter(lst-ctn-kix_82e1y4o5f3wq-2,lower-roman) ". "}.lst-kix_82e1y4o5f3wq-4 > li:before{content:"" counter(lst-ctn-kix_82e1y4o5f3wq-4,lower-latin) ". "}.lst-kix_ul8kb4iuqop2-8 > li:before{content:"" counter(lst-ctn-kix_ul8kb4iuqop2-8,lower-roman) ". "}.lst-kix_ul8kb4iuqop2-2 > li{counter-increment:lst-ctn-kix_ul8kb4iuqop2-2}.lst-kix_82e1y4o5f3wq-6 > li:before{content:"" counter(lst-ctn-kix_82e1y4o5f3wq-6,decimal) ". "}.lst-kix_byhv03d04cj2-5 > li:before{content:"" counter(lst-ctn-kix_byhv03d04cj2-5,lower-roman) ". "}.lst-kix_ul8kb4iuqop2-8 > li{counter-increment:lst-ctn-kix_ul8kb4iuqop2-8}ol.lst-kix_gw16n5qq267j-8.start{counter-reset:lst-ctn-kix_gw16n5qq267j-8 0}.lst-kix_4dcjlvssrtx3-1 > li{counter-increment:lst-ctn-kix_4dcjlvssrtx3-1}ol.lst-kix_gw16n5qq267j-1{list-style-type:none}ol.lst-kix_gw16n5qq267j-0{list-style-type:none}ol.lst-kix_gw16n5qq267j-3{list-style-type:none}.lst-kix_gw16n5qq267j-7 > li{counter-increment:lst-ctn-kix_gw16n5qq267j-7}.lst-kix_byhv03d04cj2-7 > li{counter-increment:lst-ctn-kix_byhv03d04cj2-7}ol.lst-kix_82e1y4o5f3wq-5.start{counter-reset:lst-ctn-kix_82e1y4o5f3wq-5 0}ol.lst-kix_gw16n5qq267j-2{list-style-type:none}ol.lst-kix_gw16n5qq267j-8{list-style-type:none}ol.lst-kix_gw16n5qq267j-5{list-style-type:none}ol.lst-kix_gw16n5qq267j-4{list-style-type:none}ol.lst-kix_gw16n5qq267j-7{list-style-type:none}ol.lst-kix_gw16n5qq267j-6{list-style-type:none}.lst-kix_50pmlbck485l-2 > li{counter-increment:lst-ctn-kix_50pmlbck485l-2}ol.lst-kix_50pmlbck485l-3.start{counter-reset:lst-ctn-kix_50pmlbck485l-3 0}ol.lst-kix_4dcjlvssrtx3-0.start{counter-reset:lst-ctn-kix_4dcjlvssrtx3-0 0}.lst-kix_ul8kb4iuqop2-6 > li{counter-increment:lst-ctn-kix_ul8kb4iuqop2-6}.lst-kix_byhv03d04cj2-5 > li{counter-increment:lst-ctn-kix_byhv03d04cj2-5}.lst-kix_gw16n5qq267j-0 > li:before{content:"" counter(lst-ctn-kix_gw16n5qq267j-0,decimal) ". "}ol.lst-kix_ul8kb4iuqop2-0.start{counter-reset:lst-ctn-kix_ul8kb4iuqop2-0 0}.lst-kix_gw16n5qq267j-3 > li:before{content:"" counter(lst-ctn-kix_gw16n5qq267j-3,decimal) ". "}.lst-kix_gw16n5qq267j-1 > li:before{content:"" counter(lst-ctn-kix_gw16n5qq267j-1,lower-latin) ". "}.lst-kix_gw16n5qq267j-5 > li:before{content:"" counter(lst-ctn-kix_gw16n5qq267j-5,lower-roman) ". "}.lst-kix_gw16n5qq267j-2 > li:before{content:"" counter(lst-ctn-kix_gw16n5qq267j-2,lower-roman) ". "}ol.lst-kix_gw16n5qq267j-3.start{counter-reset:lst-ctn-kix_gw16n5qq267j-3 0}.lst-kix_50pmlbck485l-0 > li{counter-increment:lst-ctn-kix_50pmlbck485l-0}.lst-kix_4dcjlvssrtx3-3 > li{counter-increment:lst-ctn-kix_4dcjlvssrtx3-3}.lst-kix_gw16n5qq267j-4 > li:before{content:"" counter(lst-ctn-kix_gw16n5qq267j-4,lower-latin) ". "}ol.lst-kix_byhv03d04cj2-3.start{counter-reset:lst-ctn-kix_byhv03d04cj2-3 0}.lst-kix_gw16n5qq267j-6 > li:before{content:"" counter(lst-ctn-kix_gw16n5qq267j-6,decimal) ". "}.lst-kix_gw16n5qq267j-7 > li:before{content:"" counter(lst-ctn-kix_gw16n5qq267j-7,lower-latin) ". "}.lst-kix_ul8kb4iuqop2-4 > li{counter-increment:lst-ctn-kix_ul8kb4iuqop2-4}.lst-kix_50pmlbck485l-6 > li{counter-increment:lst-ctn-kix_50pmlbck485l-6}.lst-kix_gw16n5qq267j-8 > li:before{content:"" counter(lst-ctn-kix_gw16n5qq267j-8,lower-roman) ". "}.lst-kix_4dcjlvssrtx3-6 > li:before{content:"" counter(lst-ctn-kix_4dcjlvssrtx3-6,decimal) ". "}.lst-kix_byhv03d04cj2-3 > li{counter-increment:lst-ctn-kix_byhv03d04cj2-3}.lst-kix_4dcjlvssrtx3-5 > li:before{content:"" counter(lst-ctn-kix_4dcjlvssrtx3-5,lower-roman) ". "}.lst-kix_4dcjlvssrtx3-5 > li{counter-increment:lst-ctn-kix_4dcjlvssrtx3-5}ol.lst-kix_50pmlbck485l-8.start{counter-reset:lst-ctn-kix_50pmlbck485l-8 0}.lst-kix_4dcjlvssrtx3-7 > li:before{content:"" counter(lst-ctn-kix_4dcjlvssrtx3-7,lower-latin) ". "}.lst-kix_4dcjlvssrtx3-8 > li:before{content:"" counter(lst-ctn-kix_4dcjlvssrtx3-8,lower-roman) ". "}ol.lst-kix_4dcjlvssrtx3-5{list-style-type:none}ol.lst-kix_4dcjlvssrtx3-6{list-style-type:none}ol.lst-kix_4dcjlvssrtx3-7{list-style-type:none}ol.lst-kix_4dcjlvssrtx3-8{list-style-type:none}.lst-kix_82e1y4o5f3wq-1 > li{counter-increment:lst-ctn-kix_82e1y4o5f3wq-1}ol.lst-kix_4dcjlvssrtx3-1{list-style-type:none}ol.lst-kix_4dcjlvssrtx3-2{list-style-type:none}ol.lst-kix_4dcjlvssrtx3-3{list-style-type:none}ol.lst-kix_4dcjlvssrtx3-4{list-style-type:none}.lst-kix_4dcjlvssrtx3-2 > li:before{content:"" counter(lst-ctn-kix_4dcjlvssrtx3-2,lower-roman) ". "}ol.lst-kix_50pmlbck485l-8{list-style-type:none}ol.lst-kix_50pmlbck485l-7{list-style-type:none}.lst-kix_4dcjlvssrtx3-3 > li:before{content:"" counter(lst-ctn-kix_4dcjlvssrtx3-3,decimal) ". "}ol.lst-kix_50pmlbck485l-6{list-style-type:none}ol.lst-kix_4dcjlvssrtx3-0{list-style-type:none}.lst-kix_4dcjlvssrtx3-4 > li:before{content:"" counter(lst-ctn-kix_4dcjlvssrtx3-4,lower-latin) ". "}ol.lst-kix_byhv03d04cj2-2.start{counter-reset:lst-ctn-kix_byhv03d04cj2-2 0}ol.lst-kix_50pmlbck485l-1{list-style-type:none}ol.lst-kix_82e1y4o5f3wq-0.start{counter-reset:lst-ctn-kix_82e1y4o5f3wq-0 0}ol.lst-kix_82e1y4o5f3wq-6.start{counter-reset:lst-ctn-kix_82e1y4o5f3wq-6 0}ol.lst-kix_50pmlbck485l-0{list-style-type:none}ol.lst-kix_50pmlbck485l-5{list-style-type:none}ol.lst-kix_50pmlbck485l-4{list-style-type:none}ol.lst-kix_50pmlbck485l-3{list-style-type:none}ol.lst-kix_50pmlbck485l-2{list-style-type:none}.lst-kix_4dcjlvssrtx3-1 > li:before{content:"" counter(lst-ctn-kix_4dcjlvssrtx3-1,lower-latin) ". "}.lst-kix_4dcjlvssrtx3-0 > li:before{content:"" counter(lst-ctn-kix_4dcjlvssrtx3-0,decimal) ". "}ol.lst-kix_byhv03d04cj2-8.start{counter-reset:lst-ctn-kix_byhv03d04cj2-8 0}.lst-kix_byhv03d04cj2-1 > li{counter-increment:lst-ctn-kix_byhv03d04cj2-1}.lst-kix_82e1y4o5f3wq-7 > li:before{content:"" counter(lst-ctn-kix_82e1y4o5f3wq-7,lower-latin) ". "}.lst-kix_gw16n5qq267j-2 > li{counter-increment:lst-ctn-kix_gw16n5qq267j-2}ol.lst-kix_82e1y4o5f3wq-1.start{counter-reset:lst-ctn-kix_82e1y4o5f3wq-1 0}ol.lst-kix_4dcjlvssrtx3-7.start{counter-reset:lst-ctn-kix_4dcjlvssrtx3-7 0}.lst-kix_82e1y4o5f3wq-1 > li:before{content:"" counter(lst-ctn-kix_82e1y4o5f3wq-1,lower-latin) ". "}.lst-kix_byhv03d04cj2-0 > li{counter-increment:lst-ctn-kix_byhv03d04cj2-0}ol.lst-kix_byhv03d04cj2-4.start{counter-reset:lst-ctn-kix_byhv03d04cj2-4 0}ol.lst-kix_gw16n5qq267j-4.start{counter-reset:lst-ctn-kix_gw16n5qq267j-4 0}.lst-kix_50pmlbck485l-8 > li{counter-increment:lst-ctn-kix_50pmlbck485l-8}.lst-kix_82e1y4o5f3wq-5 > li{counter-increment:lst-ctn-kix_82e1y4o5f3wq-5}ol.lst-kix_82e1y4o5f3wq-4.start{counter-reset:lst-ctn-kix_82e1y4o5f3wq-4 0}.lst-kix_gw16n5qq267j-1 > li{counter-increment:lst-ctn-kix_gw16n5qq267j-1}.lst-kix_gw16n5qq267j-3 > li{counter-increment:lst-ctn-kix_gw16n5qq267j-3}ol.lst-kix_ul8kb4iuqop2-4.start{counter-reset:lst-ctn-kix_ul8kb4iuqop2-4 0}ol.lst-kix_4dcjlvssrtx3-4.start{counter-reset:lst-ctn-kix_4dcjlvssrtx3-4 0}.lst-kix_byhv03d04cj2-2 > li{counter-increment:lst-ctn-kix_byhv03d04cj2-2}ol.lst-kix_byhv03d04cj2-7.start{counter-reset:lst-ctn-kix_byhv03d04cj2-7 0}ol.lst-kix_50pmlbck485l-5.start{counter-reset:lst-ctn-kix_50pmlbck485l-5 0}ol.lst-kix_ul8kb4iuqop2-7.start{counter-reset:lst-ctn-kix_ul8kb4iuqop2-7 0}.lst-kix_82e1y4o5f3wq-6 > li{counter-increment:lst-ctn-kix_82e1y4o5f3wq-6}ol.lst-kix_50pmlbck485l-2.start{counter-reset:lst-ctn-kix_50pmlbck485l-2 0}ol.lst-kix_82e1y4o5f3wq-3.start{counter-reset:lst-ctn-kix_82e1y4o5f3wq-3 0}ol.lst-kix_4dcjlvssrtx3-5.start{counter-reset:lst-ctn-kix_4dcjlvssrtx3-5 0}ol.lst-kix_50pmlbck485l-4.start{counter-reset:lst-ctn-kix_50pmlbck485l-4 0}.lst-kix_byhv03d04cj2-8 > li:before{content:"" counter(lst-ctn-kix_byhv03d04cj2-8,lower-roman) ". "}.lst-kix_byhv03d04cj2-4 > li:before{content:"" counter(lst-ctn-kix_byhv03d04cj2-4,lower-latin) ". "}.lst-kix_50pmlbck485l-8 > li:before{content:"" counter(lst-ctn-kix_50pmlbck485l-8,lower-roman) ". "}.lst-kix_byhv03d04cj2-2 > li:before{content:"" counter(lst-ctn-kix_byhv03d04cj2-2,lower-roman) ". "}.lst-kix_ul8kb4iuqop2-7 > li:before{content:"" counter(lst-ctn-kix_ul8kb4iuqop2-7,lower-latin) ". "}ol.lst-kix_gw16n5qq267j-2.start{counter-reset:lst-ctn-kix_gw16n5qq267j-2 0}ol.lst-kix_byhv03d04cj2-6.start{counter-reset:lst-ctn-kix_byhv03d04cj2-6 0}.lst-kix_4dcjlvssrtx3-4 > li{counter-increment:lst-ctn-kix_4dcjlvssrtx3-4}.lst-kix_byhv03d04cj2-0 > li:before{content:"" counter(lst-ctn-kix_byhv03d04cj2-0,decimal) ". "}.lst-kix_ul8kb4iuqop2-5 > li:before{content:"" counter(lst-ctn-kix_ul8kb4iuqop2-5,lower-roman) ". "}ol.lst-kix_ul8kb4iuqop2-6.start{counter-reset:lst-ctn-kix_ul8kb4iuqop2-6 0}.lst-kix_ul8kb4iuqop2-1 > li:before{content:"" counter(lst-ctn-kix_ul8kb4iuqop2-1,lower-latin) ". "}.lst-kix_ul8kb4iuqop2-3 > li:before{content:"" counter(lst-ctn-kix_ul8kb4iuqop2-3,decimal) ". "}.lst-kix_50pmlbck485l-1 > li{counter-increment:lst-ctn-kix_50pmlbck485l-1}.lst-kix_50pmlbck485l-7 > li{counter-increment:lst-ctn-kix_50pmlbck485l-7}ol.lst-kix_4dcjlvssrtx3-6.start{counter-reset:lst-ctn-kix_4dcjlvssrtx3-6 0}ol.lst-kix_gw16n5qq267j-1.start{counter-reset:lst-ctn-kix_gw16n5qq267j-1 0}ol.lst-kix_82e1y4o5f3wq-0{list-style-type:none}.lst-kix_82e1y4o5f3wq-3 > li:before{content:"" counter(lst-ctn-kix_82e1y4o5f3wq-3,decimal) ". "}ol.lst-kix_byhv03d04cj2-5.start{counter-reset:lst-ctn-kix_byhv03d04cj2-5 0}ol.lst-kix_82e1y4o5f3wq-5{list-style-type:none}ol.lst-kix_ul8kb4iuqop2-5.start{counter-reset:lst-ctn-kix_ul8kb4iuqop2-5 0}.lst-kix_ul8kb4iuqop2-5 > li{counter-increment:lst-ctn-kix_ul8kb4iuqop2-5}.lst-kix_82e1y4o5f3wq-5 > li:before{content:"" counter(lst-ctn-kix_82e1y4o5f3wq-5,lower-roman) ". "}ol.lst-kix_82e1y4o5f3wq-6{list-style-type:none}ol.lst-kix_82e1y4o5f3wq-7{list-style-type:none}ol.lst-kix_82e1y4o5f3wq-8{list-style-type:none}ol.lst-kix_82e1y4o5f3wq-1{list-style-type:none}ol.lst-kix_82e1y4o5f3wq-2{list-style-type:none}ol.lst-kix_82e1y4o5f3wq-3{list-style-type:none}.lst-kix_byhv03d04cj2-6 > li:before{content:"" counter(lst-ctn-kix_byhv03d04cj2-6,decimal) ". "}ol.lst-kix_82e1y4o5f3wq-4{list-style-type:none}

3.9 LogarithmsIf you want to learn more check out utb tsc

f(x) = 1nx is the inverse function to exDon't forget about the age old question of What does metacognition mean?
Don't forget about the age old question of Name the two types of synapses.

I.e in(ex) = x and einx = x, if x > 0

Don't forget about the age old question of What is the function of time?

Domain (0,)We also discuss several other topics like When is symmetry operation performed?

Range (-,)Don't forget about the age old question of real limits

Properties of Inx

  1. in(AB) = InA + inB
  2. In (Af) = pinA
  3. In (A/B) - inA - inB
  4. In 1 = 0 (since e0 = 1)
  5. In e = 1 (since e1 = e)

Suppose y = inx, x > 0

        Then x = e4

Take derivative with respect to x

        1 = ey - y1

        Y1 = 1/ey = 1/x

If x > 0 and f(x) = inx → f1(x) =

Is x < 0 and f(x) = h(-x) → f1(x) = . -1 = 1/x

If f(x) = in|x| then f1(x) = x =0

Suppose u(x) > 0

f(x) = in (u(x))

f1(x) = .u1(x)

Example: f(x) in (x3 + 10x + e4x)        u = x3 + 10x + e4x        u1 = 3x2 + 10 + 4e4x

f1(x) = =(3x2 + 10 + 4e4x) f(u) = inu        f1(u) = .

Given any function f(x) that is positive, can you write f(x) = ein(f(x)) useful?

  1. Suppose f(x) = bx for some b > 0

Then f(x) = ein(bx)        f1(x) = exinb = inb

        = exinb                 f1(x) = bx.inb

Example: f(x) = 6x        f1(x) = 6x in6

  1. Suppose f(x) = xP P any real number, x > 0

        f(x) = ein(xP)

        = epinx

f1(x) = Pinx - p -         u = pinx        f(u) = eu

        = xP . p .         u1 = p .         f1(u) = eu

        = pxp-1 [power rule]

Example:

        f(x) = x                f(x) = x → inf(x) = inx = .inx

        f1(x) = x        =(.inx + .)

                                f1(x) = f(x) (.inx + .)

Let’s find the derivative logbx        f1(x) = (.inx + .)x

If y = logbx → by = x

(b4) = (x)

B4.inb.y1 = 1 → y1 = =

**If f(x) = logbx, f1(x) =

**If f(x) = logbx, f1(x) =

Find derivative of h(x)         f(x) = g(x)        g(x) > 0

Two methods

  1. Rewrite as f(x) = ein(g(x)h(x))        f1(x) = eh(x).ing(x)

f(x) = eh(x) -in(g(x))        

  1. Apply inx to both sides

In f(x) = in(g(x)h(x)) = h(x)ing(x)

Take derivatives of both sides

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