 82.1: If logb c = a, explain why 5 2a.
 82.2: If logb c = a, explain why logb c2 5 2a.
 82.3: In 314, write each exponential equation in logarithmic form.24 5 16
 82.4: In 314, write each exponential equation in logarithmic form.. 53 5 125
 82.5: In 314, write each exponential equation in logarithmic form.64 5 82
 82.6: In 314, write each exponential equation in logarithmic form.120 5 1
 82.7: In 314, write each exponential equation in logarithmic form.216 5 63
 82.8: In 314, write each exponential equation in logarithmic form.1021 5 0.1
 82.9: In 314, write each exponential equation in logarithmic form.523 5 0...
 82.10: In 314, write each exponential equation in logarithmic form.422 5 0...
 82.11: In 314, write each exponential equation in logarithmic form.
 82.12: In 314, write each exponential equation in logarithmic form.
 82.13: In 314, write each exponential equation in logarithmic form.
 82.14: In 314, write each exponential equation in logarithmic form.
 82.15: In 1526, write each logarithmic equation in exponential form.log10 ...
 82.16: In 1526, write each logarithmic equation in exponential form.log5 1...
 82.17: In 1526, write each logarithmic equation in exponential form.log4 1...
 82.18: In 1526, write each logarithmic equation in exponential form.7 5 lo...
 82.19: In 1526, write each logarithmic equation in exponential form.5 5 lo...
 82.20: In 1526, write each logarithmic equation in exponential form.log7 1...
 82.21: In 1526, write each logarithmic equation in exponential form.log10 ...
 82.22: In 1526, write each logarithmic equation in exponential form.log100...
 82.23: In 1526, write each logarithmic equation in exponential form.22 5 l...
 82.24: In 1526, write each logarithmic equation in exponential form.
 82.25: In 1526, write each logarithmic equation in exponential form.
 82.26: In 1526, write each logarithmic equation in exponential form.
 82.27: In 2756, evaluate each logarithmic expression. Show all work.log8 8
 82.28: In 2756, evaluate each logarithmic expression. Show all work.5 log8 8
 82.29: In 2756, evaluate each logarithmic expression. Show all work.log6 216
 82.30: In 2756, evaluate each logarithmic expression. Show all work.4 log6...
 82.31: In 2756, evaluate each logarithmic expression. Show all work.log4116
 82.32: In 2756, evaluate each logarithmic expression. Show all work.
 82.33: In 2756, evaluate each logarithmic expression. Show all work.
 82.34: In 2756, evaluate each logarithmic expression. Show all work.
 82.35: In 2756, evaluate each logarithmic expression. Show all work.og3 729
 82.36: In 2756, evaluate each logarithmic expression. Show all work.
 82.37: In 2756, evaluate each logarithmic expression. Show all work.log4164
 82.38: In 2756, evaluate each logarithmic expression. Show all work.16 log...
 82.39: In 2756, evaluate each logarithmic expression. Show all work.log3 81
 82.40: In 2756, evaluate each logarithmic expression. Show all work.. log2 16
 82.41: In 2756, evaluate each logarithmic expression. Show all work.log3 8...
 82.42: In 2756, evaluate each logarithmic expression. Show all work.. log5...
 82.43: In 2756, evaluate each logarithmic expression. Show all work.log10 ...
 82.44: In 2756, evaluate each logarithmic expression. Show all work.log2 32
 82.45: In 2756, evaluate each logarithmic expression. Show all work.log1214
 82.46: In 2756, evaluate each logarithmic expression. Show all work.log3 81
 82.47: In 2756, evaluate each logarithmic expression. Show all work.log18 324
 82.48: In 2756, evaluate each logarithmic expression. Show all work.. log6 36
 82.49: In 2756, evaluate each logarithmic expression. Show all work.log13 27
 82.50: In 2756, evaluate each logarithmic expression. Show all work.6 log6...
 82.51: In 2756, evaluate each logarithmic expression. Show all work.. log5...
 82.52: In 2756, evaluate each logarithmic expression. Show all work.og3 81...
 82.53: In 2756, evaluate each logarithmic expression. Show all work.log5 2...
 82.54: In 2756, evaluate each logarithmic expression. Show all work.2 log1...
 82.55: In 2756, evaluate each logarithmic expression. Show all work.3 log3...
 82.56: In 2756, evaluate each logarithmic expression. Show all work.log3 2...
 82.57: In 5768, solve each equation for the variable.log10 x 5 3
 82.58: In 5768, solve each equation for the variable.log2 32 5 x
 82.59: In 5768, solve each equation for the variable.log5 625 5 x
 82.60: In 5768, solve each equation for the variable.a 5 log4 16
 82.61: In 5768, solve each equation for the variable.logb 27 5 3
 82.62: In 5768, solve each equation for the variable.logb 64 5 6
 82.63: In 5768, solve each equation for the variable.log5 y 5 22
 82.64: In 5768, solve each equation for the variable.log25 c 5 24
 82.65: In 5768, solve each equation for the variable.
 82.66: In 5768, solve each equation for the variable.
 82.67: In 5768, solve each equation for the variable.log36 6 5 x
 82.68: In 5768, solve each equation for the variable.logb 1,000 5
 82.69: If f(x) 5 log3 x, find f(81).
 82.70: If p(x) 5 log25 x, find p(5).
 82.71: If g(x) 5 log10 x, find g(0.001).
 82.72: If h(x) 5 log32 x, find h(8).
 82.73: Solve for a: log5 0.2 5 loga 10
 82.74: Solve for x: log100 10 5 log16 x
 82.75: When $1 is invested at 6% interest, its value, A, after t years is ...
 82.76: R is the ratio of the population of a town n years from now to the ...
 82.77: The decay constant of radium is 20.0004 per year. The amount of rad...
Solutions for Chapter 82: LOGARITHMIC FORM OF AN EXPONENTIAL EQUATION
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 82: LOGARITHMIC FORM OF AN EXPONENTIAL EQUATION
Get Full SolutionsThis textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. Chapter 82: LOGARITHMIC FORM OF AN EXPONENTIAL EQUATION includes 77 full stepbystep solutions. Since 77 problems in chapter 82: LOGARITHMIC FORM OF AN EXPONENTIAL EQUATION have been answered, more than 30953 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

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

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

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

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

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.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

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

Special solutions to As = O.
One free variable is Si = 1, other free variables = 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}.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B IIĀ·

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

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