 4.3.1: Fill in each blank so that the resulting statement is true.The prod...
 4.3.2: Fill in each blank so that the resulting statement is true.The quot...
 4.3.3: Fill in each blank so that the resulting statement is true.The powe...
 4.3.4: Fill in each blank so that the resulting statement is true.The chan...
 4.3.5: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.6: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.7: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.8: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.9: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.10: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.11: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.12: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.13: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.14: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.15: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.16: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.17: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.18: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.19: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.20: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.21: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.22: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.23: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.24: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.25: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.26: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.27: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.28: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.29: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.30: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.31: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.32: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.33: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.34: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.35: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.36: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.37: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.38: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.39: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.40: In Exercises 140, use properties of logarithms to expand eachlogari...
 4.3.41: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.42: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.43: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.44: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.45: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.46: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.47: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.48: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.49: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.50: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.51: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.52: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.53: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.54: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.55: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.56: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.57: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.58: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.59: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.60: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.61: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.62: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.63: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.64: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.65: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.66: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.67: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.68: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.69: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.70: In Exercises 4170, use properties of logarithms to condense eachlog...
 4.3.71: In Exercises 7178, use common logarithms or natural logarithmsand a...
 4.3.72: In Exercises 7178, use common logarithms or natural logarithmsand a...
 4.3.73: In Exercises 7178, use common logarithms or natural logarithmsand a...
 4.3.74: In Exercises 7178, use common logarithms or natural logarithmsand a...
 4.3.75: In Exercises 7178, use common logarithms or natural logarithmsand a...
 4.3.76: In Exercises 7178, use common logarithms or natural logarithmsand a...
 4.3.77: In Exercises 7178, use common logarithms or natural logarithmsand a...
 4.3.78: In Exercises 7178, use common logarithms or natural logarithmsand a...
 4.3.79: In Exercises 7982, use a graphing utility and the changeofbasepro...
 4.3.80: In Exercises 7982, use a graphing utility and the changeofbasepro...
 4.3.81: In Exercises 7982, use a graphing utility and the changeofbasepro...
 4.3.82: In Exercises 7982, use a graphing utility and the changeofbasepro...
 4.3.83: In Exercises 8388, let logb 2 = A and logb 3 = C. Write eachexpress...
 4.3.84: In Exercises 8388, let logb 2 = A and logb 3 = C. Write eachexpress...
 4.3.85: In Exercises 8388, let logb 2 = A and logb 3 = C. Write eachexpress...
 4.3.86: In Exercises 8388, let logb 2 = A and logb 3 = C. Write eachexpress...
 4.3.87: In Exercises 8388, let logb 2 = A and logb 3 = C. Write eachexpress...
 4.3.88: In Exercises 8388, let logb 2 = A and logb 3 = C. Write eachexpress...
 4.3.89: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.90: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.91: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.92: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.93: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.94: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.95: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.96: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.97: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.98: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.99: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.100: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.101: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.102: In Exercises 89102, determine whether each equation is true orfalse...
 4.3.103: The loudness level of a sound can be expressed by comparingthe soun...
 4.3.104: The formulat = 1c[ln A  ln(A  N)]describes the time, t, in weeks,...
 4.3.105: Describe the product rule for logarithms and give anexample.
 4.3.106: Describe the quotient rule for logarithms and give anexample.
 4.3.107: Describe the power rule for logarithms and give an example.
 4.3.108: Without showing the details, explain how to condenseln x  2 ln(x +...
 4.3.109: Describe the changeofbase property and give an example.
 4.3.110: Explain how to use your calculator to find log14 283.
 4.3.111: You overhear a student talking about a property oflogarithms in whi...
 4.3.112: Find ln 2 using a calculator. Then calculate each of thefollowing: ...
 4.3.113: a. Use a graphing utility (and the changeofbase property)to graph...
 4.3.114: Graph y = log x, y = log(10x), and y = log(0.1x) in thesame viewing...
 4.3.115: Use a graphing utility and the changeofbase property tograph y = ...
 4.3.116: Disprove each statement in Exercises 116120 bya. letting y equal a ...
 4.3.117: Disprove each statement in Exercises 116120 bya. letting y equal a ...
 4.3.118: Disprove each statement in Exercises 116120 bya. letting y equal a ...
 4.3.119: Disprove each statement in Exercises 116120 bya. letting y equal a ...
 4.3.120: Disprove each statement in Exercises 116120 bya. letting y equal a ...
 4.3.121: In Exercises 121124, determine whether eachstatement makes sense or...
 4.3.122: In Exercises 121124, determine whether eachstatement makes sense or...
 4.3.123: In Exercises 121124, determine whether eachstatement makes sense or...
 4.3.124: In Exercises 121124, determine whether eachstatement makes sense or...
 4.3.125: In Exercises 125128, determine whether each statement is trueor fal...
 4.3.126: In Exercises 125128, determine whether each statement is trueor fal...
 4.3.127: In Exercises 125128, determine whether each statement is trueor fal...
 4.3.128: In Exercises 125128, determine whether each statement is trueor fal...
 4.3.129: Use the changeofbase property to prove thatlog e = 1ln 10
 4.3.130: If log 3 = A and log 7 = B, find log7 9 in terms of A and B.
 4.3.131: Write as a single term that does not contain a logarithm:eln 8x5ln...
 4.3.132: If f(x) = logb x, show thatf(x + h)  f(x)h = logba1 +hxb1h, h 0.
 4.3.133: Use the proof of the product rule in the appendix to provethe quoti...
 4.3.134: Given f(x) = 2x + 1 and g(x) = 1x, find each of thefollowing:a. (f ...
 4.3.135: Use the Leading Coefficient Test to determine the endbehavior of th...
 4.3.136: Graph: f(x) = 4x2x2  9.(Section 3.5, Example 6)
 4.3.137: Exercises 137139 will help you prepare for the material coveredin t...
 4.3.138: Exercises 137139 will help you prepare for the material coveredin t...
 4.3.139: Exercises 137139 will help you prepare for the material coveredin t...
Solutions for Chapter 4.3: Properties of Logarithms
Full solutions for College Algebra  7th Edition
ISBN: 9780134469164
Solutions for Chapter 4.3: Properties of Logarithms
Get Full SolutionsCollege Algebra was written by and is associated to the ISBN: 9780134469164. Chapter 4.3: Properties of Logarithms includes 139 full stepbystep solutions. Since 139 problems in chapter 4.3: Properties of Logarithms have been answered, more than 32566 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 7.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

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

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 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!).

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

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

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.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

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!

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

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·

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.