 1.6.1: Which of the following equations is incorrect? (a) 32 35 = 37 (b) (...
 1.6.2: Compute logb2 (b4).
 1.6.3: When is ln x negative?
 1.6.4: What is ln(3)? Explain.
 1.6.5: Explain the phrase, The logarithm converts multiplication into addi...
 1.6.6: What are the domain and range of f (x) = ln x?
 1.6.7: Which hyperbolic functions take on only positive values?
 1.6.8: Which hyperbolic functions are increasing on their domains?
 1.6.9: Describe three properties of hyperbolic functions that have trigono...
 1.6.10: In Exercises 210, solve for the unknown variable. b2x+1 = b6
 1.6.11: In Exercises 1126, calculate without using a calculator. log3 27
 1.6.12: In Exercises 1126, calculate without using a calculator. 11. log5125
 1.6.13: In Exercises 1126, calculate without using a calculator. ln 1
 1.6.14: In Exercises 1126, calculate without using a calculator. log5(54)
 1.6.15: In Exercises 1126, calculate without using a calculator. log2(25/3)
 1.6.16: In Exercises 1126, calculate without using a calculator. log2(85/3)
 1.6.17: In Exercises 1126, calculate without using a calculator. log64 4
 1.6.18: In Exercises 1126, calculate without using a calculator. log7(492)
 1.6.19: In Exercises 1126, calculate without using a calculator. log8 2 + l...
 1.6.20: In Exercises 1126, calculate without using a calculator. log25 30 +...
 1.6.21: In Exercises 1126, calculate without using a calculator. log4 48 lo...
 1.6.22: In Exercises 1126, calculate without using a calculator. ln( e e7/5)
 1.6.23: In Exercises 1126, calculate without using a calculator. ln(e3) + l...
 1.6.24: In Exercises 1126, calculate without using a calculator. log2 4 3 +...
 1.6.25: In Exercises 1126, calculate without using a calculator. 7log7(29)
 1.6.26: In Exercises 1126, calculate without using a calculator. 83 log8(2)
 1.6.27: Write as the natural log of a single expression: (a) 2 ln 5 + 3 ln ...
 1.6.28: Solve for x: ln(x2 + 1) 3 ln x = ln(2).
 1.6.29: In Exercises 2934, solve for the unknown. 7e5t = 100
 1.6.30: In Exercises 2934, solve for the unknown. 6e4t = 2
 1.6.31: In Exercises 2934, solve for the unknown. 2x22x = 8
 1.6.32: In Exercises 2934, solve for the unknown. e2t+1 = 9e1t
 1.6.33: In Exercises 2934, solve for the unknown. ln(x4) ln(x2) = 2
 1.6.34: In Exercises 2934, solve for the unknown. log3 y + 3 log3(y2) = 14
 1.6.35: Find the inverse of y = e2x3
 1.6.36: Find the inverse of y = ln(x2 2) for x > 2.
 1.6.37: Use a calculator to compute sinh x and cosh x for x = 3, 0, 5.
 1.6.38: Compute sinh(ln 5) and tanh(3 ln 5) without using a calculator.
 1.6.39: Show, by producing a counterexample, that ln(ab) is not equal to (l...
 1.6.40: For which values of x are y = sinh x and y = cosh x increasing and ...
 1.6.41: Show that y = tanh x is an odd function.
 1.6.42: The population of a city (in millions) at time t (years) is P (t) =...
 1.6.43: The GutenbergRichter Law states that the number N of earthquakes pe...
 1.6.44: The energy E (in joules) radiated as seismic waves from an earthqua...
 1.6.45: Refer to the graphs to explain why the equation sinh x = t has a un...
 1.6.46: Compute cosh x and tanh x, assuming that sinh x = 0.8.
 1.6.47: Prove the addition formula for cosh x given by cosh(x + y) = cosh x...
 1.6.48: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh x cosh(...
 1.6.49: A train moves along a track at velocity v. Bionica walks down the a...
 1.6.50: Show that loga b logb a = 1 for all a, b > 0 such that a = 1 and b ...
 1.6.51: Verify that for all x, the formula holds. logb x = loga x loga b fo...
 1.6.52: (a) Use the addition formulas for sinh x and cosh x to prove tanh(u...
 1.6.53: Prove that every function f can be written as a sum f (x) = f+(x) +...
Solutions for Chapter 1.6: Exponential and Logarithmic Functions
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 1.6: Exponential and Logarithmic Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. Chapter 1.6: Exponential and Logarithmic Functions includes 53 full stepbystep solutions. Since 53 problems in chapter 1.6: Exponential and Logarithmic Functions have been answered, more than 41910 students have viewed full stepbystep solutions from this chapter.

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Domain of a function
The set of all input values for a function

Doubleangle identity
An identity involving a trigonometric function of 2u

equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)

Horizontal component
See Component form of a vector.

Inductive step
See Mathematical induction.

Inverse sine function
The function y = sin1 x

Line of symmetry
A line over which a graph is the mirror image of itself

Linear function
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

Natural exponential function
The function ƒ1x2 = ex.

Normal curve
The graph of ƒ(x) = ex2/2

Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22  2r1r2 cos 1?1  ?22

Quartic function
A degree 4 polynomial function.

Reexpression of data
A transformation of a data set.

Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.

Row operations
See Elementary row operations.

Vertical line test
A test for determining whether a graph is a function.