 8.1: a. Sketch the graph of f(x) 5 log3 x. b. What is the domain of f(x)...
 8.2: In 24,solve each equation for y in terms of x. x 5 log6 y
 8.3: In 24,solve each equation for y in terms of x. x 5 log2.5 y
 8.4: In 24,solve each equation for y in terms of x. x 5 82y
 8.5: In 510,write each expression in logarithmic form. 23 5 8
 8.6: In 510,write each expression in logarithmic form. 62 5 36
 8.7: In 510,write each expression in logarithmic form. 101 5 0.1
 8.8: In 510,write each expression in logarithmic form. .
 8.9: In 510,write each expression in logarithmic form. 4 5
 8.10: In 510,write each expression in logarithmic form. 5 22
 8.11: In 1116,write each expression in exponential form. log3 81 5 4
 8.12: In 1116,write each expression in exponential form. log5 125 5 3
 8.13: In 1116,write each expression in exponential form. log4 8 5
 8.14: In 1116,write each expression in exponential form. .
 8.15: In 1116,write each expression in exponential form. 21 5 log 0.1
 8.16: In 1116,write each expression in exponential form. . 0 5 ln 1
 8.17: In 1720,evaluate each logarithmic expression.Show all work. 3 log2 8
 8.18: In 1720,evaluate each logarithmic expression.Show all work. 14 9 lo...
 8.19: In 1720,evaluate each logarithmic expression.Show all work. log3 4
 8.20: In 1720,evaluate each logarithmic expression.Show all work. log2 25...
 8.21: If f(x) 5 log3 x,find f(27).
 8.22: If f(x) 5 log x,find f(0.01).
 8.23: If f(x) 5 log4 x,find f(32).
 8.24: If f(x) 5 ln x,find f(e4).
 8.25: In 2532,if log 5 5 a and log 3 5 b,express each log in terms of a a...
 8.26: In 2532,if log 5 5 a and log 3 5 b,express each log in terms of a a...
 8.27: In 2532,if log 5 5 a and log 3 5 b,express each log in terms of a a...
 8.28: In 2532,if log 5 5 a and log 3 5 b,express each log in terms of a a...
 8.29: In 2532,if log 5 5 a and log 3 5 b,express each log in terms of a a...
 8.30: In 2532,if log 5 5 a and log 3 5 b,express each log in terms of a a...
 8.31: In 2532,if log 5 5 a and log 3 5 b,express each log in terms of a a...
 8.32: In 2532,if log 5 5 a and log 3 5 b,express each log in terms of a a...
 8.33: If b . 1,then what is the value of logb b?
 8.34: If log a 5 0.5,what is log (100a)?
 8.35: In 3540,solve each equation for the variable.Show all work. . x 5 l...
 8.36: In 3540,solve each equation for the variable.Show all work. logb 27 5
 8.37: In 3540,solve each equation for the variable.Show all work. log6 x ...
 8.38: In 3540,solve each equation for the variable.Show all work. log 0.0...
 8.39: In 3540,solve each equation for the variable.Show all work. log25 x 5
 8.40: In 3540,solve each equation for the variable.Show all work. logb 16...
 8.41: In 4144:a.Write each expression as a single logarithm.b.Find the va...
 8.42: In 4144:a.Write each expression as a single logarithm.b.Find the va...
 8.43: In 4144:a.Write each expression as a single logarithm.b.Find the va...
 8.44: In 4144:a.Write each expression as a single logarithm.b.Find the va...
 8.45: In 4547: a. Expand each expression using the properties of logarith...
 8.46: In 4547: a. Expand each expression using the properties of logarith...
 8.47: In 4547: a. Expand each expression using the properties of logarith...
 8.48: In 4853,write an equation for A in terms of x and y. log A 5 log x ...
 8.49: In 4853,write an equation for A in terms of x and y. log2 A 5 log2 ...
 8.50: In 4853,write an equation for A in terms of x and y. ln x 5 ln y 2 ...
 8.51: In 4853,write an equation for A in terms of x and y. log5 A 5 log5 ...
 8.52: In 4853,write an equation for A in terms of x and y. log A 5 2(log ...
 8.53: In 4853,write an equation for A in terms of x and y. ln x 5 ln A 2
 8.54: In 5456,if log x 5 1.5,find the value of each logarithm. log 100x
 8.55: In 5456,if log x 5 1.5,find the value of each logarithm. log x2
 8.56: In 5456,if log x 5 1.5,find the value of each logarithm. log !x
 8.57: If log x 5 log 3 2 log (x 2 2),find the value of x.
 8.58: For what value of a does 1 1 log3 a 2 log3 2 5 log3 (a 1 1)?
 8.59: If 2 log (x 1 1) 5 log 5,find x to the nearest hundredth.
 8.60: In 2000,it was estimated that there were 50 rabbits in the local pa...
 8.61: When Tobey was born,his parents invested $2,000 in a fund that paid...
 8.62: The population of a small town is decreasing at the rate of 2% per ...
Solutions for Chapter 8: Logarithmic Functions
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 8: Logarithmic Functions
Get Full SolutionsChapter 8: Logarithmic Functions includes 62 full stepbystep solutions. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. Since 62 problems in chapter 8: Logarithmic Functions have been answered, more than 28434 students have viewed full stepbystep solutions from this chapter. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. This expansive textbook survival guide covers the following chapters and their solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·