 3.2.3.2.1: The inverse function of the exponential function is called the ____...
 3.2.3.2.2: The common logarithmic function has base _______ .
 3.2.3.2.3: The logarithmic function is called the _______ function.
 3.2.3.2.4: The inverse property of logarithms states that and _______ .
 3.2.3.2.5: The onetoone property of natural logarithms states that if then _...
 3.2.3.2.6: In Exercises 1 6, write the logarithmic equation in exponential for...
 3.2.3.2.7: In Exercises 712, write the logarithmic equation in exponential for...
 3.2.3.2.8: In Exercises 712, write the logarithmic equation in exponential for...
 3.2.3.2.9: In Exercises 712, write the logarithmic equation in exponential for...
 3.2.3.2.10: In Exercises 712, write the logarithmic equation in exponential for...
 3.2.3.2.11: In Exercises 712, write the logarithmic equation in exponential for...
 3.2.3.2.12: In Exercises 712, write the logarithmic equation in exponential for...
 3.2.3.2.13: In Exercises 1318, write the exponential equation in logarithmic fo...
 3.2.3.2.14: In Exercises 1318, write the exponential equation in logarithmic fo...
 3.2.3.2.15: In Exercises 1318, write the exponential equation in logarithmic fo...
 3.2.3.2.16: In Exercises 1318, write the exponential equation in logarithmic fo...
 3.2.3.2.17: In Exercises 1318, write the exponential equation in logarithmic fo...
 3.2.3.2.18: In Exercises 1318, write the exponential equation in logarithmic fo...
 3.2.3.2.19: In Exercises 1924, write the exponential equation in logarithmic fo...
 3.2.3.2.20: In Exercises 1924, write the exponential equation in logarithmic fo...
 3.2.3.2.21: In Exercises 1924, write the exponential equation in logarithmic fo...
 3.2.3.2.22: In Exercises 1924, write the exponential equation in logarithmic fo...
 3.2.3.2.23: In Exercises 1924, write the exponential equation in logarithmic fo...
 3.2.3.2.24: In Exercises 1924, write the exponential equation in logarithmic fo...
 3.2.3.2.25: In Exercises 2528, evaluate the function at the indicated value of ...
 3.2.3.2.26: In Exercises 2528, evaluate the function at the indicated value of ...
 3.2.3.2.27: In Exercises 2528, evaluate the function at the indicated value of ...
 3.2.3.2.28: In Exercises 2528, evaluate the function at the indicated value of ...
 3.2.3.2.29: In Exercises 29 32, use a calculator to evaluate the function at th...
 3.2.3.2.30: In Exercises 29 32, use a calculator to evaluate the function at th...
 3.2.3.2.31: In Exercises 29 32, use a calculator to evaluate the function at th...
 3.2.3.2.32: In Exercises 29 32, use a calculator to evaluate the function at th...
 3.2.3.2.33: In Exercises 3338, solve the equation for x.
 3.2.3.2.34: In Exercises 3338, solve the equation for x.
 3.2.3.2.35: In Exercises 3338, solve the equation for x.
 3.2.3.2.36: In Exercises 3338, solve the equation for x.
 3.2.3.2.37: In Exercises 3338, solve the equation for x.
 3.2.3.2.38: In Exercises 3338, solve the equation for x.
 3.2.3.2.39: In Exercises 39 42, use the properties of logarithms to rewrite the...
 3.2.3.2.40: In Exercises 39 42, use the properties of logarithms to rewrite the...
 3.2.3.2.41: In Exercises 39 42, use the properties of logarithms to rewrite the...
 3.2.3.2.42: In Exercises 39 42, use the properties of logarithms to rewrite the...
 3.2.3.2.43: In Exercises 43 46, sketch the graph of Then use the graph of to sk...
 3.2.3.2.44: In Exercises 43 46, sketch the graph of Then use the graph of to sk...
 3.2.3.2.45: In Exercises 43 46, sketch the graph of Then use the graph of to sk...
 3.2.3.2.46: In Exercises 43 46, sketch the graph of Then use the graph of to sk...
 3.2.3.2.47: In Exercises 4752, find the domain, vertical asymptote, and xinter...
 3.2.3.2.48: In Exercises 4752, find the domain, vertical asymptote, and xinter...
 3.2.3.2.49: In Exercises 4752, find the domain, vertical asymptote, and xinter...
 3.2.3.2.50: In Exercises 4752, find the domain, vertical asymptote, and xinter...
 3.2.3.2.51: In Exercises 4752, find the domain, vertical asymptote, and xinter...
 3.2.3.2.52: In Exercises 4752, find the domain, vertical asymptote, and xinter...
 3.2.3.2.53: Library of Parent Functions In Exercises 5356, use the graph of to ...
 3.2.3.2.54: Library of Parent Functions In Exercises 5356, use the graph of to ...
 3.2.3.2.55: Library of Parent Functions In Exercises 5356, use the graph of to ...
 3.2.3.2.56: Library of Parent Functions In Exercises 5356, use the graph of to ...
 3.2.3.2.57: In Exercises 5762, use the graph of to describe the transformation ...
 3.2.3.2.58: In Exercises 5762, use the graph of to describe the transformation ...
 3.2.3.2.59: In Exercises 5762, use the graph of to describe the transformation ...
 3.2.3.2.60: In Exercises 5762, use the graph of to describe the transformation ...
 3.2.3.2.61: In Exercises 5762, use the graph of to describe the transformation ...
 3.2.3.2.62: In Exercises 5762, use the graph of to describe the transformation ...
 3.2.3.2.63: In Exercises 6366, use a calculator to evaluate the function at the...
 3.2.3.2.64: In Exercises 6366, use a calculator to evaluate the function at the...
 3.2.3.2.65: In Exercises 6366, use a calculator to evaluate the function at the...
 3.2.3.2.66: In Exercises 6366, use a calculator to evaluate the function at the...
 3.2.3.2.67: In Exercises 6770, use the properties of natural logarithms to rewr...
 3.2.3.2.68: In Exercises 6770, use the properties of natural logarithms to rewr...
 3.2.3.2.69: In Exercises 6770, use the properties of natural logarithms to rewr...
 3.2.3.2.70: In Exercises 6770, use the properties of natural logarithms to rewr...
 3.2.3.2.71: In Exercises 7174, find the domain, vertical asymptote, and interc...
 3.2.3.2.72: In Exercises 7174, find the domain, vertical asymptote, and interc...
 3.2.3.2.73: In Exercises 7174, find the domain, vertical asymptote, and interc...
 3.2.3.2.74: In Exercises 7174, find the domain, vertical asymptote, and interc...
 3.2.3.2.75: In Exercises 7580, use the graph of to describe the transformation ...
 3.2.3.2.76: In Exercises 7580, use the graph of to describe the transformation ...
 3.2.3.2.77: In Exercises 7580, use the graph of to describe the transformation ...
 3.2.3.2.78: In Exercises 7580, use the graph of to describe the transformation ...
 3.2.3.2.79: In Exercises 7580, use the graph of to describe the transformation ...
 3.2.3.2.80: In Exercises 7580, use the graph of to describe the transformation ...
 3.2.3.2.81: In Exercises 8190, (a) use a graphing utility to graph the function...
 3.2.3.2.82: In Exercises 8190, (a) use a graphing utility to graph the function...
 3.2.3.2.83: In Exercises 8190, (a) use a graphing utility to graph the function...
 3.2.3.2.84: In Exercises 8190, (a) use a graphing utility to graph the function...
 3.2.3.2.85: In Exercises 8190, (a) use a graphing utility to graph the function...
 3.2.3.2.86: In Exercises 8190, (a) use a graphing utility to graph the function...
 3.2.3.2.87: In Exercises 8190, (a) use a graphing utility to graph the function...
 3.2.3.2.88: In Exercises 8190, (a) use a graphing utility to graph the function...
 3.2.3.2.89: In Exercises 8190, (a) use a graphing utility to graph the function...
 3.2.3.2.90: In Exercises 8190, (a) use a graphing utility to graph the function...
 3.2.3.2.91: Human Memory Model Students in a mathematics class were given an ex...
 3.2.3.2.92: Data Analysis The table shows the temperatures (in ) at which water...
 3.2.3.2.93: Compound Interest A principal invested at and compounded continuous...
 3.2.3.2.94: Population The time in years for the world population to double if ...
 3.2.3.2.95: Sound Intensity The relationship between the number of decibels and...
 3.2.3.2.96: Home Mortgage The model approximates the length of a home mortgage ...
 3.2.3.2.97: Ventilation Rates In Exercises 97 and 98, use the model which appro...
 3.2.3.2.98: Ventilation Rates In Exercises 97 and 98, use the model which appro...
 3.2.3.2.99: True or False? In Exercises 99 and 100, determine whether the state...
 3.2.3.2.100: True or False? In Exercises 99 and 100, determine whether the state...
 3.2.3.2.101: Think About It In Exercises 101104, find the value of the base b so...
 3.2.3.2.102: Think About It In Exercises 101104, find the value of the base b so...
 3.2.3.2.103: Think About It In Exercises 101104, find the value of the base b so...
 3.2.3.2.104: Think About It In Exercises 101104, find the value of the base b so...
 3.2.3.2.105: Library of Parent Functions In Exercises 105 and 106, determine whi...
 3.2.3.2.106: Library of Parent Functions In Exercises 105 and 106, determine whi...
 3.2.3.2.107: Writing Explain why is defined only for 0 < a < 1 a > 1.
 3.2.3.2.108: Graphical Analysis Use a graphing utility to graph and in the same ...
 3.2.3.2.109: Exploration The following table of values was obtained by evaluatin...
 3.2.3.2.110: Pattern Recognition (a) Use a graphing utility to compare the graph...
 3.2.3.2.111: Numerical and Graphical Analysis (a) Use a graphing utility to comp...
 3.2.3.2.112: Writing Use a graphing utility to determine how many months it woul...
 3.2.3.2.113: In Exercises 113120, factor the polynomial.
 3.2.3.2.114: In Exercises 113120, factor the polynomial.
 3.2.3.2.115: In Exercises 113120, factor the polynomial.
 3.2.3.2.116: In Exercises 113120, factor the polynomial.
 3.2.3.2.117: In Exercises 113120, factor the polynomial.
 3.2.3.2.118: In Exercises 113120, factor the polynomial.
 3.2.3.2.119: In Exercises 113120, factor the polynomial.
 3.2.3.2.120: In Exercises 113120, factor the polynomial.
 3.2.3.2.121: In Exercises 121124, evaluate the function for and
 3.2.3.2.122: In Exercises 121124, evaluate the function for and
 3.2.3.2.123: In Exercises 121124, evaluate the function for and
 3.2.3.2.124: In Exercises 121124, evaluate the function for and
 3.2.3.2.125: In Exercises 125128, solve the equation graphicallIy.
 3.2.3.2.126: In Exercises 125128, solve the equation graphicallIy.
 3.2.3.2.127: In Exercises 125128, solve the equation graphicallIy.
 3.2.3.2.128: In Exercises 125128, solve the equation graphicallIy.
Solutions for Chapter 3.2: Logarithmic Functions and Their Graphs
Full solutions for Precalculus With Limits A Graphing Approach  5th Edition
ISBN: 9780618851522
Solutions for Chapter 3.2: Logarithmic Functions and Their Graphs
Get Full SolutionsThis textbook survival guide was created for the textbook: Precalculus With Limits A Graphing Approach, edition: 5. Since 128 problems in chapter 3.2: Logarithmic Functions and Their Graphs have been answered, more than 48080 students have viewed full stepbystep solutions from this chapter. Precalculus With Limits A Graphing Approach was written by and is associated to the ISBN: 9780618851522. Chapter 3.2: Logarithmic Functions and Their Graphs includes 128 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

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

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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 ().

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.