 9.2.1: Write each equation in logarithmic form
 9.2.2: Write each equation in logarithmic form
 9.2.3: Write each equation in logarithmic form
 9.2.4: Write each equation in exponential form
 9.2.5: Write each equation in exponential form
 9.2.6: Write each equation in exponential form
 9.2.7: Evaluate each expression
 9.2.8: Evaluate each expression
 9.2.9: Evaluate each expression
 9.2.10: Solve each equation. Check your solutions
 9.2.11: Solve each equation. Check your solutions
 9.2.12: Solve each equation. Check your solutions
 9.2.13: Solve 130 = 10 l og 10 R to find the relative intensity of a firewo...
 9.2.14: Solve 75 = 10 l og 10 R to find the relative intensity of a concert...
 9.2.15: How many times more intense is the fireworks display than the conce...
 9.2.16: Solve each inequality. Check your solutions.
 9.2.17: Solve each inequality. Check your solutions.
 9.2.18: Solve each inequality. Check your solutions.
 9.2.19: Solve each equation. Check your solutions.
 9.2.20: Solve each equation. Check your solutions.
 9.2.21: Solve each inequality. Check your solutions
 9.2.22: Solve each inequality. Check your solutions
 9.2.23: Write each equation in exponential form.
 9.2.24: Write each equation in exponential form.
 9.2.25: Write each equation in exponential form.
 9.2.26: Write each equation in exponential form.
 9.2.27: Write each equation in exponential form.
 9.2.28: Write each equation in exponential form.
 9.2.29: Write each equation in logarithmic form.
 9.2.30: Write each equation in logarithmic form.
 9.2.31: Write each equation in logarithmic form.
 9.2.32: Write each equation in logarithmic form.
 9.2.33: Write each equation in logarithmic form.
 9.2.34: Write each equation in logarithmic form.
 9.2.35: Evaluate each expression.
 9.2.36: Evaluate each expression.
 9.2.37: Evaluate each expression.
 9.2.38: Evaluate each expression.
 9.2.39: Evaluate each expression.
 9.2.40: Evaluate each expression.
 9.2.41: Evaluate each expression.
 9.2.42: Evaluate each expression.
 9.2.43: Evaluate each expression.
 9.2.44: Solve each equation. Check your solutions.
 9.2.45: Solve each equation. Check your solutions.
 9.2.46: Solve each equation. Check your solutions.
 9.2.47: Solve each equation. Check your solutions.
 9.2.48: Solve each equation. Check your solutions.
 9.2.49: Solve each equation. Check your solutions.
 9.2.50: The loudest animal sounds are the lowfrequency pulses made by blue...
 9.2.51: The loudest insect is the African cicada that produces a calling so...
 9.2.52: Solve each equation or inequality. Check your solutions
 9.2.53: Solve each equation or inequality. Check your solutions
 9.2.54: Solve each equation or inequality. Check your solutions
 9.2.55: Solve each equation or inequality. Check your solutions
 9.2.56: Solve each equation or inequality. Check your solutions
 9.2.57: Solve each equation or inequality. Check your solutions
 9.2.58: Solve each equation or inequality. Check your solutions
 9.2.59: Solve each equation or inequality. Check your solutions
 9.2.60: Show that each statement is true.
 9.2.61: Show that each statement is true.
 9.2.62: Show that each statement is true.
 9.2.63: Sketch the graphs of y = lo g _1 2 x and y = (_1 2) x on the same a...
 9.2.64: Sketch the graphs of y = log3 x, y = log3 (x + 2), y = log3 x  3. ...
 9.2.65: How many times as great is the amplitude caused by an earthquake wi...
 9.2.66: How many times as great was the motion caused by the 1906 San Franc...
 9.2.67: A proposed city ordinance will make it illegal to create sound in a...
 9.2.68: Use a graphing calculator to sketch the graphs on the same screen. ...
 9.2.69: What are a reasonable domain and range for each function?
 9.2.70: What are a reasonable domain and range for each function?
 9.2.71: Find the expression that does not belong. Explain.
 9.2.72: Paul and Clemente are solving lo g 3 x = 9. Who is correct? Explain...
 9.2.73: Using the definition of a logarithmic function where y = l og b x, ...
 9.2.74: Use the information about sound on page 509 to explain how a logari...
 9.2.75: What is the equation of the function? A y = 2(3 ) x B y = 2 (_1 3) ...
 9.2.76: What is the solution to the equation 3x = 11? F x = 2 G x = log10 2...
 9.2.77: Simplify each expression
 9.2.78: Simplify each expression
 9.2.79: Solve each equation. Check your solutions
 9.2.80: Solve each equation. Check your solutions
 9.2.81: Solve each equation by using the method of your choice. Find exact ...
 9.2.82: Solve each equation by using the method of your choice. Find exact ...
 9.2.83: Donna Bowers has $8000 she wants to save in the bank. A 12month ce...
 9.2.84: Simplify. Assume that no variable equals zero
 9.2.85: Simplify. Assume that no variable equals zero
 9.2.86: Simplify. Assume that no variable equals zero
 9.2.87: Simplify. Assume that no variable equals zero
Solutions for Chapter 9.2: Logarithms and Logarithmic Functions
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 9.2: Logarithms and Logarithmic Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1. Since 87 problems in chapter 9.2: Logarithms and Logarithmic Functions have been answered, more than 44430 students have viewed full stepbystep solutions from this chapter. Chapter 9.2: Logarithms and Logarithmic Functions includes 87 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. California Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568.

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

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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

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.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

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

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

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).

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

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.