 5.2.65: In Exercises 5966, write the exponential equation inlogarithmic for...
 5.2.66: In Exercises 5966, write the exponential equation inlogarithmic for...
 5.2.67: In Exercises 6770, use a calculator to evaluate the functionat the ...
 5.2.68: In Exercises 6770, use a calculator to evaluate the functionat the ...
 5.2.69: In Exercises 6770, use a calculator to evaluate the functionat the ...
 5.2.70: In Exercises 6770, use a calculator to evaluate the functionat the ...
 5.2.71: In Exercises 7174, evaluate at the indicatedvalue of without using ...
 5.2.72: In Exercises 7174, evaluate at the indicatedvalue of without using ...
 5.2.73: In Exercises 7174, evaluate at the indicatedvalue of without using ...
 5.2.74: In Exercises 7174, evaluate at the indicatedvalue of without using ...
 5.2.75: In Exercises 7578, find the domain, intercept, and verticalasympto...
 5.2.76: In Exercises 7578, find the domain, intercept, and verticalasympto...
 5.2.77: In Exercises 7578, find the domain, intercept, and verticalasympto...
 5.2.78: In Exercises 7578, find the domain, intercept, and verticalasympto...
 5.2.79: In Exercises 7984, use a graphing utility to graph thefunction. Be ...
 5.2.80: In Exercises 7984, use a graphing utility to graph thefunction. Be ...
 5.2.81: In Exercises 7984, use a graphing utility to graph thefunction. Be ...
 5.2.82: In Exercises 7984, use a graphing utility to graph thefunction. Be ...
 5.2.83: In Exercises 7984, use a graphing utility to graph thefunction. Be ...
 5.2.84: In Exercises 7984, use a graphing utility to graph thefunction. Be ...
 5.2.85: In Exercises 8592, use the OnetoOne Property to solve theequation...
 5.2.86: In Exercises 8592, use the OnetoOne Property to solve theequation...
 5.2.87: In Exercises 8592, use the OnetoOne Property to solve theequation...
 5.2.88: In Exercises 8592, use the OnetoOne Property to solve theequation...
 5.2.89: In Exercises 8592, use the OnetoOne Property to solve theequation...
 5.2.90: In Exercises 8592, use the OnetoOne Property to solve theequation...
 5.2.91: In Exercises 8592, use the OnetoOne Property to solve theequation...
 5.2.92: In Exercises 8592, use the OnetoOne Property to solve theequation...
 5.2.93: MONTHLY PAYMENT The modelapproximates the length of a home mortgage...
 5.2.94: COMPOUND INTEREST A principal invested atand compounded continuousl...
 5.2.95: CABLE TELEVISION The numbers of cable televisionsystems (in thousan...
 5.2.96: POPULATION The time in years for the worldpopulation to double if i...
 5.2.97: HUMAN MEMORY MODEL Students in a mathematicsclass were given an exa...
 5.2.98: SOUND INTENSITY The relationship between thenumber of decibels and ...
 5.2.99: TRUE OR FALSE? In Exercises 99 and 100, determinewhether the statem...
 5.2.100: TRUE OR FALSE? In Exercises 99 and 100, determinewhether the statem...
 5.2.101: In Exercises 101104, sketch the graphs of and anddescribe the relat...
 5.2.102: In Exercises 101104, sketch the graphs of and anddescribe the relat...
 5.2.103: In Exercises 101104, sketch the graphs of and anddescribe the relat...
 5.2.104: In Exercises 101104, sketch the graphs of and anddescribe the relat...
 5.2.105: THINK ABOUT IT Complete the table forComplete the table forCompare ...
 5.2.106: GRAPHICAL ANALYSIS Use a graphing utility tograph and in the same v...
 5.2.107: (a) Complete the table for the function given by(b) Use the table i...
 5.2.108: CAPSTONE The table of values was obtained byevaluating a function. ...
 5.2.109: WRITING Explain why is defined only for
 5.2.110: In Exercises 110 and 111, (a) use a graphing utility to graphthe fu...
 5.2.111: In Exercises 110 and 111, (a) use a graphing utility to graphthe fu...
 5.2.45: f x log x 3 x 2
 5.2.46: f x log3 f x log x
 5.2.47: f x log x 1 3x 2
 5.2.48: f x log3f x log x 1
 5.2.49: f x log x 31 x
 5.2.50: f x log3f x log xv
 5.2.51: In Exercises 5158, write the logarithmic equation inexponential form.
 5.2.52: In Exercises 5158, write the logarithmic equation inexponential form.
 5.2.53: In Exercises 5158, write the logarithmic equation inexponential form.
 5.2.54: In Exercises 5158, write the logarithmic equation inexponential form.
 5.2.55: In Exercises 5158, write the logarithmic equation inexponential form.
 5.2.56: In Exercises 5158, write the logarithmic equation inexponential form.
 5.2.57: In Exercises 5158, write the logarithmic equation inexponential form.
 5.2.58: In Exercises 5158, write the logarithmic equation inexponential form.
 5.2.59: In Exercises 5966, write the exponential equation inlogarithmic for...
 5.2.60: In Exercises 5966, write the exponential equation inlogarithmic for...
 5.2.61: In Exercises 5966, write the exponential equation inlogarithmic for...
 5.2.62: In Exercises 5966, write the exponential equation inlogarithmic for...
 5.2.63: In Exercises 5966, write the exponential equation inlogarithmic for...
 5.2.64: In Exercises 5966, write the exponential equation inlogarithmic for...
Solutions for Chapter 5.2: Logarithmic Functions and Their Graphs
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter 5.2: Logarithmic Functions and Their Graphs
Get Full SolutionsSince 67 problems in chapter 5.2: Logarithmic Functions and Their Graphs have been answered, more than 29641 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9781439048696. This textbook survival guide was created for the textbook: College Algebra , edition: 8. Chapter 5.2: Logarithmic Functions and Their Graphs includes 67 full stepbystep solutions. 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).

Column space C (A) =
space of all combinations of the columns of A.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

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

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

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  ).

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

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

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

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

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

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).

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 ().

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).