 94.1: log 4
 94.2: log 23
 94.3: log 0.5
 94.4: NUTRITION For health reasons, Sandras doctor has told her to avoid ...
 94.5: 9 x = 45
 94.6: 3.1 a  3 = 9.42
 94.7: 11 x 2 = 25.4
 94.8: 7 t  2 = 5t
 94.9: 4 5n > 30
 94.10: 4 p  1 3 p
 94.11: log 7 5
 94.12: log 3 42
 94.13: log 2 9
 94.14: log 5
 94.15: log 12
 94.16: log 7.2
 94.17: log 2.3
 94.18: log 0.8
 94.19: log 0.03
 94.20: POLLUTION The acidity of water determines the toxic effects of runo...
 94.21: BUILDING DESIGN The 1971 Sylmar earthquake in Los Angeles had a Ric...
 94.22: 5 x = 52
 94.23: 4 3p = 10
 94.24: 3 n + 2 = 14.5
 94.25: 9 z  4 = 6.28
 94.26: 8 .2 n  3 = 42.5
 94.27: 2.1 t  5 = 9.32
 94.28: 6 x 42
 94.29: 8 2a < 124
 94.30: 4 3x 72
 94.31: 8 2n > 5 2 4n + 3
 94.32: 7 p + 2 1 3 5 p
 94.33: 3 y + 2 8 3y
 94.34: log 2 13
 94.35: log 5 20
 94.36: log 7 3
 94.37: log 3 8
 94.38: log 4 (1. 6)
 94.39: log 6 5
 94.40: ammonia: [ H +] = 1 1 0 11 mole per liter
 94.41: vinegar: [ H +] = 6.3 1 0 3 mole per liter
 94.42: lemon juice: [ H +] = 7.9 1 0 3 mole per liter
 94.43: orange juice: [H +] = 3.16 1 0 4 mole per liter
 94.44: 20 x 2 = 70
 94.45: 2x2  3 = 15
 94.46: 2 2x + 3 = 3 3x
 94.47: 1 6 d  4 = 3 3 d
 94.48: 5 5y  2 = 2 2y + 1
 94.49: 8 2x  5 = 5 x + 1
 94.50: 2 n = 3 n  2
 94.51: 4 x = 5 x + 2
 94.52: 3 y = 2 y  1
 94.53: Find the interval in cents when the frequency changes from 443 Hert...
 94.54: If the interval is 55 cents and the beginning frequency is 225 Hz, ...
 94.55: If Marta adds no more money to the account, how long will it take t...
 94.56: How long will it take for Martas money to double?
 94.57: CHALLENGE Solve log a 3 = loga x for x and explain each step.
 94.58: Write log5 _ 9 log5 3 as a single logarithm.
 94.59: CHALLENGE a. Find the values of log 2 8 and log 8 2. b. Find the va...
 94.60: Writing in Math Use the information about acidity of common substan...
 94.61: ACT/SAT If 2 4 = 3 x , then what is the approximate value of x? A 0...
 94.62: REVIEW Which equation is equivalent to log4 _1 16 = x? F 1_ 4 16 = ...
 94.63: log 7 16
 94.64: log 7 27
 94.65: log 7 36
 94.66: log 4 r = 3
 94.67: log 8 z 2
 94.68: log 3 (4x  5) = 5
 94.69: Use synthetic substitution to find f(2) for f(x) = x 3 + 6x  2.
 94.70: MONEY Viviana has two dollars worth of nickels, dimes, and quarters...
 94.71: log 2 3 = x
 94.72: log 3 x = 2
 94.73: log 5 125 = 3
Solutions for Chapter 94: Common Logarithms
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 94: Common Logarithms
Get Full SolutionsChapter 94: Common Logarithms includes 73 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. Since 73 problems in chapter 94: Common Logarithms have been answered, more than 53541 students have viewed full stepbystep solutions from this chapter.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

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.)

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

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.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

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

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.

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

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

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.

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).

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

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.