 6.4.1: Solve each inequality: (a) (b) x 2  x  6 7 0 3x  7 8  2x
 6.4.2: Solve the inequalityx  1 x + 4 7 0
 6.4.3: Solve: 2x + 3 = 9
 6.4.4: The domain of the logarithmic function isf1x2 = loga x
 6.4.5: The graph of every logarithmic function where and passes through th...
 6.4.6: If the graph of a logarithmic function where and is increasing, the...
 6.4.7: True or False If y = log . a x, then y = ax
 6.4.8: True or False The graph of and a Z 1, has an xintercept equal to 1...
 6.4.9: In 916, change each exponential statement to an equivalent statemen...
 6.4.10: In 916, change each exponential statement to an equivalent statemen...
 6.4.11: In 916, change each exponential statement to an equivalent statemen...
 6.4.12: In 916, change each exponential statement to an equivalent statemen...
 6.4.13: In 916, change each exponential statement to an equivalent statemen...
 6.4.14: In 916, change each exponential statement to an equivalent statemen...
 6.4.15: In 916, change each exponential statement to an equivalent statemen...
 6.4.16: In 916, change each exponential statement to an equivalent statemen...
 6.4.17: In 1724, change each logarithmic statement to an equivalent stateme...
 6.4.18: In 1724, change each logarithmic statement to an equivalent stateme...
 6.4.19: In 1724, change each logarithmic statement to an equivalent stateme...
 6.4.20: In 1724, change each logarithmic statement to an equivalent stateme...
 6.4.21: In 1724, change each logarithmic statement to an equivalent stateme...
 6.4.22: In 1724, change each logarithmic statement to an equivalent stateme...
 6.4.23: In 1724, change each logarithmic statement to an equivalent stateme...
 6.4.24: In 1724, change each logarithmic statement to an equivalent stateme...
 6.4.25: In 2536, find the exact value of each logarithm without using a cal...
 6.4.26: In 2536, find the exact value of each logarithm without using a cal...
 6.4.27: In 2536, find the exact value of each logarithm without using a cal...
 6.4.28: In 2536, find the exact value of each logarithm without using a cal...
 6.4.29: In 2536, find the exact value of each logarithm without using a cal...
 6.4.30: In 2536, find the exact value of each logarithm without using a cal...
 6.4.31: In 2536, find the exact value of each logarithm without using a cal...
 6.4.32: In 2536, find the exact value of each logarithm without using a cal...
 6.4.33: In 2536, find the exact value of each logarithm without using a cal...
 6.4.34: In 2536, find the exact value of each logarithm without using a cal...
 6.4.35: In 2536, find the exact value of each logarithm without using a cal...
 6.4.36: In 2536, find the exact value of each logarithm without using a cal...
 6.4.37: In 3748, find the domain of each function. f1x2 = ln1x  32
 6.4.38: In 3748, find the domain of each function. g1x2 = ln1x  12
 6.4.39: In 3748, find the domain of each function. F1x2 = log2 x2
 6.4.40: In 3748, find the domain of each function. H1x2 = log5 x3
 6.4.41: In 3748, find the domain of each function. f1x2 = 3  2 log4 cx2  5 d
 6.4.42: In 3748, find the domain of each function. g1x2 = 8 + 5 ln12x + 32
 6.4.43: In 3748, find the domain of each function. f1x2 = lna 1x + 1b
 6.4.44: In 3748, find the domain of each function. g1x2 = lna 1x  5b
 6.4.45: In 3748, find the domain of each function. g1x2 = log5 ax + 1x b
 6.4.46: In 3748, find the domain of each function. h1x2 = log3 a xx  1b
 6.4.47: In 3748, find the domain of each function. f1x2 = 2ln x
 6.4.48: In 3748, find the domain of each function. g1x2 = 1ln x
 6.4.49: In 4956, use a calculator to evaluate each expression. Round your a...
 6.4.50: In 4956, use a calculator to evaluate each expression. Round your a...
 6.4.51: In 4956, use a calculator to evaluate each expression. Round your a...
 6.4.52: In 4956, use a calculator to evaluate each expression. Round your a...
 6.4.53: In 4956, use a calculator to evaluate each expression. Round your a...
 6.4.54: In 4956, use a calculator to evaluate each expression. Round your a...
 6.4.55: In 4956, use a calculator to evaluate each expression. Round your a...
 6.4.56: In 4956, use a calculator to evaluate each expression. Round your a...
 6.4.57: Find a so that the graph of f1x2 = loga x contains the point 2, 2 .
 6.4.58: Find a so that the graph of f1x2 = log x contains the pointa 1 2 4b.
 6.4.59: In 5962, graph each function and its inverse on the same Cartesian ...
 6.4.60: In 5962, graph each function and its inverse on the same Cartesian ...
 6.4.61: In 5962, graph each function and its inverse on the same Cartesian ...
 6.4.62: In 5962, graph each function and its inverse on the same Cartesian ...
 6.4.63: In 6370, the graph of a logarithmic function is given. Match each g...
 6.4.64: In 6370, the graph of a logarithmic function is given. Match each g...
 6.4.65: In 6370, the graph of a logarithmic function is given. Match each g...
 6.4.66: In 6370, the graph of a logarithmic function is given. Match each g...
 6.4.67: In 6370, the graph of a logarithmic function is given. Match each g...
 6.4.68: In 6370, the graph of a logarithmic function is given. Match each g...
 6.4.69: In 6370, the graph of a logarithmic function is given. Match each g...
 6.4.70: In 6370, the graph of a logarithmic function is given. Match each g...
 6.4.71: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.72: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.73: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.74: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.75: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.76: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.77: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.78: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.79: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.80: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.81: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.82: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.83: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.84: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.85: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.86: In 7186, use the given function f to: (a) Find the domain of f. (b)...
 6.4.87: In 87110,solve each equation. log3 x = 2
 6.4.88: In 87110,solve each equation. log5 x = 3
 6.4.89: In 87110,solve each equation. log212x + 12 = 3
 6.4.90: In 87110,solve each equation. log313x  22 = 2
 6.4.91: In 87110,solve each equation. logx4 = 2
 6.4.92: In 87110,solve each equation. logx a18b = 3
 6.4.93: In 87110,solve each equation. ln ex = 5
 6.4.94: In 87110,solve each equation. ln e2x = 8
 6.4.95: In 87110,solve each equation. log4 64 = x
 6.4.96: In 87110,solve each equation. log5 625 = x
 6.4.97: In 87110,solve each equation. log3 243 = 2x + 1
 6.4.98: In 87110,solve each equation. log6 36 = 5x + 3
 6.4.99: In 87110,solve each equation. e3x = 10
 6.4.100: In 87110,solve each equation. e2x = 13
 6.4.101: In 87110,solve each equation. e2x+5 = 8
 6.4.102: In 87110,solve each equation. e2x+1 = 13
 6.4.103: In 87110,solve each equation. log31x2 + 12 = 2
 6.4.104: In 87110,solve each equation. log51x2 + x + 42 = 2
 6.4.105: In 87110,solve each equation. log2 8x = 3
 6.4.106: In 87110,solve each equation. log3 3x = 1
 6.4.107: In 87110,solve each equation. 5e0.2x = 7
 6.4.108: In 87110,solve each equation. 8 # 102x7 = 3
 6.4.109: In 87110,solve each equation. 2 # 102x = 5
 6.4.110: In 87110,solve each equation. 4ex+1 = 5
 6.4.111: Suppose that (a) What is the domain of G? (b) What is G(40)? What p...
 6.4.112: Suppose that (a) What is the domain of F? (b) What is F(7)? What po...
 6.4.113: In 113116, graph each function. Based on the graph,state the domain...
 6.4.114: In 113116, graph each function. Based on the graph,state the domain...
 6.4.115: In 113116, graph each function. Based on the graph,state the domain...
 6.4.116: In 113116, graph each function. Based on the graph,state the domain...
 6.4.117: Chemistry The pH of a chemical solution is given by the formula whe...
 6.4.118: Diversity Index Shannons diversity index is a measure of the divers...
 6.4.119: Atmospheric Pressure The atmospheric pressure p on an object decrea...
 6.4.120: Healing of Wounds The normal healing of wounds can be modeled by an...
 6.4.121: Exponential Probability Between 12:00 PM and 1:00 PM, cars arrive a...
 6.4.122: Exponential Probability Between 5:00 PM and 6:00 PM, cars arrive at...
 6.4.123: Drug Medication The formula can be used to find the number of milli...
 6.4.124: Spreading of Rumors A model for the number N of people in a college...
 6.4.125: Current in a RL Circuit The equation governing the amount of curren...
 6.4.126: Learning Curve Psychologists sometimes use the function to measure ...
 6.4.127: Loudness of Sound 127130 use the following discussion: The loudness...
 6.4.128: Loudness of Sound 127130 use the following discussion: The loudness...
 6.4.129: Loudness of Sound 127130 use the following discussion: The loudness...
 6.4.130: Loudness of Sound 127130 use the following discussion: The loudness...
 6.4.131: The Richter Scale 131 and 132 use the following discussion: The Ric...
 6.4.132: The Richter Scale 131 and 132 use the following discussion: The Ric...
 6.4.133: Alcohol and Driving The concentration of alcohol in a persons blood...
 6.4.134: Is there any function of the form that increases more slowly than a...
 6.4.135: In the definition of the logarithmic function, the base a is not al...
 6.4.136: Critical Thinking In buying a new car, one consideration might be h...
Solutions for Chapter 6.4: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 6.4
Get Full SolutionsAlgebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. This expansive textbook survival guide covers the following chapters and their solutions. Since 136 problems in chapter 6.4 have been answered, more than 55675 students have viewed full stepbystep solutions from this chapter. Chapter 6.4 includes 136 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9.

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.)

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

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

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.

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.

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.

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

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

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

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

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.