 6.3.1: What is a base b logarithm? Discuss the meaning by interpreting eac...
 6.3.2: How is the logarithmic function f(x) = logb (x) related to the expo...
 6.3.3: How can the logarithmic equation logb x = y be solved for x using t...
 6.3.4: Discuss the meaning of the common logarithm. What is its relationsh...
 6.3.5: Discuss the meaning of the natural logarithm. What is its relations...
 6.3.6: For the following exercises, rewrite each equation in exponential f...
 6.3.7: For the following exercises, rewrite each equation in exponential f...
 6.3.8: For the following exercises, rewrite each equation in exponential f...
 6.3.9: For the following exercises, rewrite each equation in exponential f...
 6.3.10: For the following exercises, rewrite each equation in exponential f...
 6.3.11: For the following exercises, rewrite each equation in exponential f...
 6.3.12: For the following exercises, rewrite each equation in exponential f...
 6.3.13: For the following exercises, rewrite each equation in exponential f...
 6.3.14: For the following exercises, rewrite each equation in exponential f...
 6.3.15: For the following exercises, rewrite each equation in exponential f...
 6.3.16: For the following exercises, rewrite each equation in logarithmic f...
 6.3.17: For the following exercises, rewrite each equation in logarithmic f...
 6.3.18: For the following exercises, rewrite each equation in logarithmic f...
 6.3.19: For the following exercises, rewrite each equation in logarithmic f...
 6.3.20: For the following exercises, rewrite each equation in logarithmic f...
 6.3.21: For the following exercises, rewrite each equation in logarithmic f...
 6.3.22: For the following exercises, rewrite each equation in logarithmic f...
 6.3.23: For the following exercises, rewrite each equation in logarithmic f...
 6.3.24: For the following exercises, rewrite each equation in logarithmic f...
 6.3.25: For the following exercises, rewrite each equation in logarithmic f...
 6.3.26: For the following exercises, solve for x by converting the logarith...
 6.3.27: For the following exercises, solve for x by converting the logarith...
 6.3.28: For the following exercises, solve for x by converting the logarith...
 6.3.29: For the following exercises, solve for x by converting the logarith...
 6.3.30: For the following exercises, solve for x by converting the logarith...
 6.3.31: For the following exercises, solve for x by converting the logarith...
 6.3.32: For the following exercises, solve for x by converting the logarith...
 6.3.33: For the following exercises, solve for x by converting the logarith...
 6.3.34: For the following exercises, solve for x by converting the logarith...
 6.3.35: For the following exercises, solve for x by converting the logarith...
 6.3.36: For the following exercises, use the definition of common and natur...
 6.3.37: For the following exercises, use the definition of common and natur...
 6.3.38: For the following exercises, use the definition of common and natur...
 6.3.39: For the following exercises, use the definition of common and natur...
 6.3.40: For the following exercises, use the definition of common and natur...
 6.3.41: For the following exercises, use the definition of common and natur...
 6.3.42: For the following exercises, evaluate the base b logarithmic expres...
 6.3.43: For the following exercises, evaluate the base b logarithmic expres...
 6.3.44: For the following exercises, evaluate the base b logarithmic expres...
 6.3.45: For the following exercises, evaluate the base b logarithmic expres...
 6.3.46: For the following exercises, evaluate the common logarithmic expres...
 6.3.47: For the following exercises, evaluate the common logarithmic expres...
 6.3.48: For the following exercises, evaluate the common logarithmic expres...
 6.3.49: For the following exercises, evaluate the common logarithmic expres...
 6.3.50: For the following exercises, evaluate the natural logarithmic expre...
 6.3.51: For the following exercises, evaluate the natural logarithmic expre...
 6.3.52: For the following exercises, evaluate the natural logarithmic expre...
 6.3.53: For the following exercises, evaluate the natural logarithmic expre...
 6.3.54: For the following exercises, evaluate each expression using a calcu...
 6.3.55: For the following exercises, evaluate each expression using a calcu...
 6.3.56: For the following exercises, evaluate each expression using a calcu...
 6.3.57: For the following exercises, evaluate each expression using a calcu...
 6.3.58: For the following exercises, evaluate each expression using a calcu...
 6.3.59: Is x = 0 in the domain of the function f(x) = log(x)? If so, what i...
 6.3.60: Is f(x) = 0 in the range of the function f (x) = log(x)? If so, for...
 6.3.61: Is there a number x such that ln x = 2? If so, what is that number?...
 6.3.62: Is the following true: log3 _ (27) log4 _ 1 64 = 1? Verify the result.
 6.3.63: Is the following true: ln(e1.725 _ ) ln(1) = 1.725? Verify the result.
 6.3.64: The exposure index EI for a 35 millimeter camera is a measurement o...
 6.3.65: Refer to the previous exercise. Suppose the light meter on a camera...
 6.3.66: The intensity levels I of two earthquakes measured on a seismograph...
Solutions for Chapter 6.3: LOGARITHMIC FUNCTIONS
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 6.3: LOGARITHMIC FUNCTIONS
Get Full SolutionsCollege Algebra was written by and is associated to the ISBN: 9781938168383. Since 66 problems in chapter 6.3: LOGARITHMIC FUNCTIONS have been answered, more than 32315 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra, edition: 1. Chapter 6.3: LOGARITHMIC FUNCTIONS includes 66 full stepbystep solutions.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

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

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.

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

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

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

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» 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.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

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