 5.4.1: Exer. 12: Change to logarithmic form.
 5.4.2: Exer. 12: Change to logarithmic form.
 5.4.3: Exer. 34: Change to exponential form.
 5.4.4: Exer. 34: Change to exponential form.
 5.4.5: Exer. 510: Solve for t using logarithms with base a.
 5.4.6: Exer. 510: Solve for t using logarithms with base a.
 5.4.7: Exer. 510: Solve for t using logarithms with base a.
 5.4.8: Exer. 510: Solve for t using logarithms with base a.
 5.4.9: Exer. 510: Solve for t using logarithms with base a.
 5.4.10: Exer. 510: Solve for t using logarithms with base a.
 5.4.11: Exer. 1112: Change to logarithmic form.
 5.4.12: Exer. 1112: Change to logarithmic form.
 5.4.13: Exer. 1314: Change to exponential form.
 5.4.14: Exer. 1314: Change to exponential form.
 5.4.15: Exer. 1516: Find the number, if possible
 5.4.16: Exer. 1516: Find the number, if possible
 5.4.17: Exer. 1718: Find the number
 5.4.18: Exer. 1718: Find the number
 5.4.19: Exer. 1934: Solve the equation.
 5.4.20: Exer. 1934: Solve the equation.
 5.4.21: Exer. 1934: Solve the equation.
 5.4.22: Exer. 1934: Solve the equation.
 5.4.23: Exer. 1934: Solve the equation.
 5.4.24: Exer. 1934: Solve the equation.
 5.4.25: Exer. 1934: Solve the equation.
 5.4.26: Exer. 1934: Solve the equation.
 5.4.27: Exer. 1934: Solve the equation.
 5.4.28: Exer. 1934: Solve the equation.
 5.4.29: Exer. 1934: Solve the equation.
 5.4.30: Exer. 1934: Solve the equation.
 5.4.31: Exer. 1934: Solve the equation.
 5.4.32: Exer. 1934: Solve the equation.
 5.4.33: Exer. 1934: Solve the equation.
 5.4.34: Exer. 1934: Solve the equation.
 5.4.35: Sketch the graph of f if :
 5.4.36: Work Exercise 35 if
 5.4.37: Exer. 3742: Sketch the graph of f.
 5.4.38: Exer. 3742: Sketch the graph of f.
 5.4.39: Exer. 3742: Sketch the graph of f.
 5.4.40: Exer. 3742: Sketch the graph of f.
 5.4.41: Exer. 3742: Sketch the graph of f.
 5.4.42: Exer. 3742: Sketch the graph of f.
 5.4.43: Exer. 4344: Find a logarithmic function of the form for the given g...
 5.4.44: Exer. 4344: Find a logarithmic function of the form for the given g...
 5.4.45: Exer. 4550: Shown in the figure is the graph of a function f. Expre...
 5.4.46: Exer. 4550: Shown in the figure is the graph of a function f. Expre...
 5.4.47: Exer. 4550: Shown in the figure is the graph of a function f. Expre...
 5.4.48: Exer. 4550: Shown in the figure is the graph of a function f. Expre...
 5.4.49: Exer. 4550: Shown in the figure is the graph of a function f. Expre...
 5.4.50: Exer. 4550: Shown in the figure is the graph of a function f. Expre...
 5.4.51: Exer. 5152: Approximate x to three significant figures.
 5.4.52: Exer. 5152: Approximate x to three significant figures.
 5.4.53: Change to an exponential function with base e and approximate the g...
 5.4.54: Change to an exponential function with base e and approximate the d...
 5.4.55: If we start with milligrams of radium, the amount q remaining after...
 5.4.56: The radioactive bismuth isotope disintegrates according to , where ...
 5.4.57: A schematic of a simple electrical circuit consisting of a resistor...
 5.4.58: An electrical condenser with initial charge is allowed to discharge...
 5.4.59: Use the Richter scale formula to find the magnitude of an earthquak...
 5.4.60: Refer to Exercise 59. The largest recorded magnitudes of earthquake...
 5.4.61: The loudness of a sound, as experienced by the human ear, is based ...
 5.4.62: Refer to Exercise 61. A sound intensity level of 140 decibels produ...
 5.4.63: The population (in millions) of the United States t years after 198...
 5.4.64: The population (in millions) of India t years after 1985 may be app...
 5.4.65: The Ehrenberg relation is an empirically based formula relating the...
 5.4.66: If interest is compounded continuously at the rate of 6% per year, ...
 5.4.67: The air pressure (in ) at an altitude of h feet above sea level may...
 5.4.68: A liquids vapor pressure P (in ), a measure of its volatility, is r...
 5.4.69: The weight W (in kilograms) of a female African elephant at age t (...
 5.4.70: A country presently has coal reserves of 50 million tons. Last year...
 5.4.71: An urban density model is a formula that relates the population den...
 5.4.72: Stars are classified into categories of brightness called magnitude...
 5.4.73: Radioactive iodine is frequently used in tracer studies involving t...
 5.4.74: Radioactive strontium has been deposited in a large field by acid r...
 5.4.75: In a survey of 15 cities ranging in population P from 300 to 3,000,...
 5.4.76: For manufacturers of computer chips, it is important to consider th...
 5.4.77: Exer. 7778: Approximate the function at the value of x to four deci...
 5.4.78: Exer. 7778: Approximate the function at the value of x to four deci...
 5.4.79: Studies relating serum cholesterol level to coronary heart disease ...
 5.4.80: Refer to Exercise 79. For a male, the risk can be approximated by t...
Solutions for Chapter 5.4: Logarithmic Functions
Full solutions for Algebra and Trigonometry with Analytic Geometry  12th Edition
ISBN: 9780495559719
Solutions for Chapter 5.4: Logarithmic Functions
Get Full SolutionsChapter 5.4: Logarithmic Functions includes 80 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry with Analytic Geometry was written by and is associated to the ISBN: 9780495559719. Since 80 problems in chapter 5.4: Logarithmic Functions have been answered, more than 33461 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry with Analytic Geometry, edition: 12.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

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.

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

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

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.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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.

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.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

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

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.

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.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

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·