 B.2.B.2.2: Write each of the following equations in logarithmic form.24 =16
 B.2.B.2.3: Write each of the following equations in logarithmic form.24 =16
 B.2.B.2.4: Write each of the following equations in logarithmic form.12553
 B.2.B.2.5: Write each of the following equations in logarithmic form.16=42
 B.2.B.2.6: Write each of the following equations in logarithmic form.O.oJ 102
 B.2.B.2.7: Write each of the following equations in logarithmic form.0.001 = 103
 B.2.B.2.8: Write each of the following equations in logarithmic form.25=1 32
 B.2.B.2.9: Write each of the following equations in logarithmic form.42 1 16
 B.2.B.2.10: Write each of the following equations in logarithmic form.123 = 8
 B.2.B.2.11: Write each of the following equations in logarithmic form.':3 = 9
 B.2.B.2.12: Write each of the following equations in logarithmic form.27=33
 B.2.B.2.13: Write each of the following equations in logarithmic form.81=34
 B.2.B.2.14: Write each of the following equations in exponential form.loglO 100 2
 B.2.B.2.15: Write each of the following equations in exponential form.log2 8 = 3
 B.2.B.2.16: Write each of the following equations in exponential form.log264 = 6
 B.2.B.2.17: Write each of the following equations in exponential form.log232 5
 B.2.B.2.18: Write each of the following equations in exponential form.logs 1 = 0
 B.2.B.2.19: Write each of the following equations in exponential form.log99 = 1
 B.2.B.2.20: Write each of the following equations in exponential form.log636 = 2
 B.2.B.2.21: Write each of the following equations in exponential form.log749 2
 B.2.B.2.22: Write each of the following equations in exponential form.10glO 0.0...
 B.2.B.2.23: Write each of the following equations in exponential form.10glO 0.0...
 B.2.B.2.24: Write each of the following equations in exponential form.logs 25 2
 B.2.B.2.25: Write each of the following equations in exponential form.10g3 81 = 4
 B.2.B.2.26: Solve each of the following equations for x.log) x = 2
 B.2.B.2.27: Solve each of the following equations for x.log4 x = 3
 B.2.B.2.28: Solve each of the following equations for x.log5 x = 3
 B.2.B.2.29: Solve each of the following equations for x.log2 x = 4
 B.2.B.2.30: Solve each of the following equations for x.log2 16 = x
 B.2.B.2.31: Solve each of the following equations for x.log327 = x
 B.2.B.2.32: Solve each of the following equations for x.logs 2 = x
 B.2.B.2.33: Solve each of the following equations for x.log2s 5 = x
 B.2.B.2.34: Solve each of the following equations for x.logx 4 2
 B.2.B.2.35: Solve each of the following equations for x.10& 16 = 4
 B.2.B.2.36: Solve each of the following equations for x.logx 5 = 3
 B.2.B.2.37: Solve each of the following equations for x.logx 8 2
 B.2.B.2.38: Sketch the graph of each of the following logarithmic equations.y l...
 B.2.B.2.39: Sketch the graph of each of the following logarithmic equations.y =...
 B.2.B.2.40: Sketch the graph of each of the following logarithmic equations.y =...
 B.2.B.2.41: Sketch the graph of each of the following logarithmic equations.y l...
 B.2.B.2.42: Use your graphing calculator to graph each exponential function wit...
 B.2.B.2.43: Use your graphing calculator to graph each exponential function wit...
 B.2.B.2.44: Use your graphing calculator to graph each exponential function wit...
 B.2.B.2.45: Use your graphing calculator to graph each exponential function wit...
 B.2.B.2.46: Simplify each of the following. log2 16
 B.2.B.2.47: Simplify each of the following. log39
 B.2.B.2.48: Simplify each of the following. log25 125
 B.2.B.2.49: Simplify each of the following. 10g927
 B.2.B.2.50: Simplify each of the following. 10gIO 1,000
 B.2.B.2.51: Simplify each of the following. 10glO 10,000
 B.2.B.2.52: Simplify each of the following. log33
 B.2.B.2.53: Simplify each of the following. 10g44
 B.2.B.2.54: Simplify each of the following. logs 1
 B.2.B.2.55: Simplify each of the following. 10gIO 1
 B.2.B.2.56: Simplify each of the following. log3 (log6 6)
 B.2.B.2.57: Simplify each of the following. 10g5 (lOg3 3)
 B.2.B.2.58: MeasuringAcidity In chemistry, the pH ofa solution is defined in te...
 B.2.B.2.59: MeasuringAcidity In chemistry, the pH ofa solution is defined in te...
 B.2.B.2.60: MeasuringAcidity In chemistry, the pH ofa solution is defined in te...
 B.2.B.2.61: MeasuringAcidity In chemistry, the pH ofa solution is defined in te...
 B.2.B.2.62: Magnitude of an Earthquake Find the magnitude M of an earthquake wi...
 B.2.B.2.63: Magnitude of an Earthquake Find the magnitude M of an earthquake wi...
 B.2.B.2.64: Shock Wave If an earthquake has a magnitude of 8 on the Richter sca...
 B.2.B.2.65: Shock Wave If an earthquake has a magnitude of 6 on the Richter sca...
 B.2.B.2.66: The graph of the exponential function y = f(x) = IT is shown in Fig...
 B.2.B.2.67: The graph of the exponential function y = f(x) IT is shown in Figur...
Solutions for Chapter B.2: Exponential and Logarithmic Functions
Full solutions for Trigonometry
ISBN: 9780495108351
Solutions for Chapter B.2: Exponential and Logarithmic Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter B.2: Exponential and Logarithmic Functions includes 66 full stepbystep solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: . Trigonometry was written by and is associated to the ISBN: 9780495108351. Since 66 problems in chapter B.2: Exponential and Logarithmic Functions have been answered, more than 29855 students have viewed full stepbystep solutions from this chapter.

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 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).

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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.

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.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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.

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).

Outer product uv T
= column times row = rank one matrix.

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).

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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

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