 5.3.1: Make a handdrawn graph of each of the following. Then check your w...
 5.3.2: Make a handdrawn graph of each of the following. Then check your w...
 5.3.3: Make a handdrawn graph of each of the following. Then check your w...
 5.3.4: Make a handdrawn graph of each of the following. Then check your w...
 5.3.5: Make a handdrawn graph of each of the following. Then check your w...
 5.3.6: Make a handdrawn graph of each of the following. Then check your w...
 5.3.7: Make a handdrawn graph of each of the following. Then check your w...
 5.3.8: Make a handdrawn graph of each of the following. Then check your w...
 5.3.9: Find each of the following. Do not use a calculator.log2 16
 5.3.10: Find each of the following. Do not use a calculator.log3 9
 5.3.11: Find each of the following. Do not use a calculator.vlog5 125
 5.3.12: Find each of the following. Do not use a calculator.log2 64
 5.3.13: Find each of the following. Do not use a calculator.log 0.001
 5.3.14: Find each of the following. Do not use a calculator.log 100
 5.3.15: Find each of the following. Do not use a calculator.log2 1 4
 5.3.16: Find each of the following. Do not use a calculator.log8 2
 5.3.17: Find each of the following. Do not use a calculator.ln 1
 5.3.18: Find each of the following. Do not use a calculator.ln e
 5.3.19: Find each of the following. Do not use a calculator. log 10
 5.3.20: Find each of the following. Do not use a calculator.log 1
 5.3.21: Find each of the following. Do not use a calculator.log5 54
 5.3.22: Find each of the following. Do not use a calculator.log210
 5.3.23: Find each of the following. Do not use a calculator.log324 3
 5.3.24: Find each of the following. Do not use a calculator.log 108/5
 5.3.25: Find each of the following. Do not use a calculator.log 107
 5.3.26: Find each of the following. Do not use a calculator.log5 1
 5.3.27: Find each of the following. Do not use a calculator.log49 7
 5.3.28: Find each of the following. Do not use a calculator.log3 32
 5.3.29: Find each of the following. Do not use a calculator.ln e3/4
 5.3.30: Find each of the following. Do not use a calculator.log222
 5.3.31: Find each of the following. Do not use a calculator. log4 1
 5.3.32: Find each of the following. Do not use a calculator.ln e5
 5.3.33: Find each of the following. Do not use a calculator.ln2e
 5.3.34: Find each of the following. Do not use a calculator.log64 4
 5.3.35: Convert to a logarithmic equation.103 = 1000
 5.3.36: Convert to a logarithmic equation.53 = 1 125
 5.3.37: Convert to a logarithmic equation.81/3 = 2
 5.3.38: Convert to a logarithmic equation.100.3010 = 2
 5.3.39: Convert to a logarithmic equation.e3 = t
 5.3.40: Convert to a logarithmic equation.Qt = x
 5.3.41: Convert to a logarithmic equation.e2 = 7.3891
 5.3.42: Convert to a logarithmic equation.e1 = 0.3679
 5.3.43: Convert to a logarithmic equation.pk = 3
 5.3.44: Convert to a logarithmic equation.et = 4000
 5.3.45: Convert to an exponential equation.log5 5 = 1
 5.3.46: Convert to an exponential equation.t = log4 7
 5.3.47: Convert to an exponential equation.log 0.01 = 2
 5.3.48: Convert to an exponential equation. log 7 = 0.845
 5.3.49: Convert to an exponential equation.ln 30 = 3.4012
 5.3.50: Convert to an exponential equation.ln 0.38 = 0.9676
 5.3.51: Convert to an exponential equation.loga M = x
 5.3.52: Convert to an exponential equation.logt Q = k
 5.3.53: Convert to an exponential equation.loga T 3 = x
 5.3.54: Convert to an exponential equation.ln W 5 = t
 5.3.55: Find each of the following using a calculator. Round to four decima...
 5.3.56: Find each of the following using a calculator. Round to four decima...
 5.3.57: Find each of the following using a calculator. Round to four decima...
 5.3.58: Find each of the following using a calculator. Round to four decima...
 5.3.59: Find each of the following using a calculator. Round to four decima...
 5.3.60: Find each of the following using a calculator. Round to four decima...
 5.3.61: Find each of the following using a calculator. Round to four decima...
 5.3.62: Find each of the following using a calculator. Round to four decima...
 5.3.63: Find each of the following using a calculator. Round to four decima...
 5.3.64: Find each of the following using a calculator. Round to four decima...
 5.3.65: Find each of the following using a calculator. Round to four decima...
 5.3.66: Find each of the following using a calculator. Round to four decima...
 5.3.67: Find each of the following using a calculator. Round to four decima...
 5.3.68: Find each of the following using a calculator. Round to four decima...
 5.3.69: Find the logarithm using common logarithms and the changeofbase f...
 5.3.70: Find the logarithm using common logarithms and the changeofbase f...
 5.3.71: Find the logarithm using common logarithms and the changeofbase f...
 5.3.72: Find the logarithm using common logarithms and the changeofbase f...
 5.3.73: Find the logarithm using common logarithms and the changeofbase f...
 5.3.74: Find the logarithm using common logarithms and the changeofbase f...
 5.3.75: Find the logarithm using natural logarithms and the changeofbase ...
 5.3.76: Find the logarithm using natural logarithms and the changeofbase ...
 5.3.77: Find the logarithm using natural logarithms and the changeofbase ...
 5.3.78: Find the logarithm using natural logarithms and the changeofbase ...
 5.3.79: Graph the function and its inverse using the same set of axes. Use ...
 5.3.80: Graph the function and its inverse using the same set of axes. Use ...
 5.3.81: Graph the function and its inverse using the same set of axes. Use ...
 5.3.82: Graph the function and its inverse using the same set of axes. Use ...
 5.3.83: For each of the following functions, briefly describe how the graph...
 5.3.84: For each of the following functions, briefly describe how the graph...
 5.3.85: For each of the following functions, briefly describe how the graph...
 5.3.86: For each of the following functions, briefly describe how the graph...
 5.3.87: For each of the following functions, briefly describe how the graph...
 5.3.88: For each of the following functions, briefly describe how the graph...
 5.3.89: For each of the following functions, briefly describe how the graph...
 5.3.90: For each of the following functions, briefly describe how the graph...
 5.3.91: For each of the following functions, briefly describe how the graph...
 5.3.92: For each of the following functions, briefly describe how the graph...
 5.3.93: Graph the piecewise function.g1x2 = b 5, for x 0, log x + 1, for x 7 0
 5.3.94: Graph the piecewise function.f 1x2 = b 1  x, for x 1, ln 1x + 12,...
 5.3.95: Walking Speed. Refer to Example 12. Various cities and their popula...
 5.3.96: Forgetting. Students in a computer science class took a final exam ...
 5.3.97: Earthquake Magnitude. Refer to Example 13. Various locations of ear...
 5.3.98: pH of Substances in Chemistry. In chemistry, the pH of a substance ...
 5.3.99: Find the hydrogen ion concentration of each substance, given the pH...
 5.3.100: Advertising. A model for advertising response is given by the funct...
 5.3.101: Loudness of Sound. The loudness L, in bels (after Alexander Graham ...
 5.3.102: Find the slope and the yintercept of the line.3x  10y = 14
 5.3.103: Find the slope and the yintercept of the line.y = 6
 5.3.104: Find the slope and the yintercept of the line.x = 4
 5.3.105: Use synthetic division to find the function values.g1x2 = x3  6x2 ...
 5.3.106: Use synthetic division to find the function values.f 1x2 = x4  2x3...
 5.3.107: Find a polynomial function of degree 3 with the given numbers as ze...
 5.3.108: Find a polynomial function of degree 3 with the given numbers as ze...
 5.3.109: Simplify. log5 8 log5 2
 5.3.110: Simplify.log3 64 log3 16
 5.3.111: Find the domain of the function.f 1x2 = log5 x3
 5.3.112: Find the domain of the function.f 1x2 = log4 x2
 5.3.113: Find the domain of the function.f 1x2 = ln x
 5.3.114: Find the domain of the function.f 1x2 = log 13x  42
 5.3.115: Solve.log2 12x + 52 6 0
 5.3.116: Solve.log2 1x  32 4
 5.3.117: In Exercises 117120, match the equation with one of the figures (a)...
 5.3.118: In Exercises 117120, match the equation with one of the figures (a)...
 5.3.119: In Exercises 117120, match the equation with one of the figures (a)...
 5.3.120: In Exercises 117120, match the equation with one of the figures (a)...
 5.3.121: For Exercises 121124: a) Graph the function. b) Estimate the zeros....
 5.3.122: For Exercises 121124: a) Graph the function. b) Estimate the zeros....
 5.3.123: For Exercises 121124: a) Graph the function. b) Estimate the zeros....
 5.3.124: For Exercises 121124: a) Graph the function. b) Estimate the zeros....
 5.3.125: Using a graphing calculator, find the point(s) of intersection of t...
Solutions for Chapter 5.3: Logarithmic Functions and Graphs
Full solutions for College Algebra: Graphs and Models  5th Edition
ISBN: 9780321783950
Solutions for Chapter 5.3: Logarithmic Functions and Graphs
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra: Graphs and Models, edition: 5. Chapter 5.3: Logarithmic Functions and Graphs includes 125 full stepbystep solutions. College Algebra: Graphs and Models was written by and is associated to the ISBN: 9780321783950. This expansive textbook survival guide covers the following chapters and their solutions. Since 125 problems in chapter 5.3: Logarithmic Functions and Graphs have been answered, more than 29573 students have viewed full stepbystep solutions from this chapter.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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).

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

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

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

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

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

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

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 ().

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

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·

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).