 B.3.B.3.3: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.4: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.5: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.6: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.7: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.8: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.9: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.10: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.11: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.12: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.13: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.14: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.15: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.16: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.17: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.18: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.19: Use the three properties of logarithms given in this section to exp...
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 B.3.B.3.21: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.22: Use the three properties of logarithms given in this section to exp...
 B.3.B.3.23: Write each expression as a single logarithm.10gb x + 10gb z
 B.3.B.3.24: Write each expression as a single logarithm.10gb x  10gb Z
 B.3.B.3.25: Write each expression as a single logarithm.2 log3 x  3 log3 y
 B.3.B.3.26: Write each expression as a single logarithm.4 log2 x + 5 log2 Y
 B.3.B.3.27: Write each expression as a single logarithm.2 10glO x + '3 loglO y
 B.3.B.3.28: Write each expression as a single logarithm.3 10glO x "4 10glO Y
 B.3.B.3.29: Write each expression as a single logarithm.3log2 x + 2 log2Y log2z
 B.3.B.3.30: Write each expression as a single logarithm.2 log3 x + 3 log3 y 10g3 Z
 B.3.B.3.31: Write each expression as a single logarithm.'21 log2 x  310gzy 410...
 B.3.B.3.32: Write each expression as a single logarithm.3 10glO x 10glO Y 10gIO Z
 B.3.B.3.33: Write each expression as a single logarithm.2 loglO x  "4 10glO Y ...
 B.3.B.3.34: Write each expression as a single logarithm.3 log 10 x  '3 loglO Y...
 B.3.B.3.35: Solve each of the following equations.log2x + log23 = 1
 B.3.B.3.36: Solve each of the following equations.log3 x + log3 3 = 1
 B.3.B.3.37: Solve each of the following equations.log3x  IOg3 2 = 2
 B.3.B.3.38: Solve each of the following equations.log3 x + log3 2 2
 B.3.B.3.39: Solve each of the following equations.log3x + log3 (x  2) = 1
 B.3.B.3.40: Solve each of the following equations.log6 x + log6 (x 1) = 1
 B.3.B.3.41: Solve each of the following equations.log3 (x + 3) log3 (x  1) = 1
 B.3.B.3.42: Solve each of the following equations.log4 (x 2)  log4 (x + 1) = 1
 B.3.B.3.43: Solve each of the following equations.log2 x + log2 (x 2) = 3
 B.3.B.3.44: Solve each of the following equations.log4 x + log4 (x + 6) 2
 B.3.B.3.45: Solve each of the following equations.logg x + logs (x 3) = "3
 B.3.B.3.46: Solve each of the following equations.IOg27 X + log27 (x + 8) 2 3
 B.3.B.3.47: Solve each of the following equations.log5 Vx + log5 = 1
 B.3.B.3.48: Solve each of the following equations.log2 Vx + logz V6x + 5=1
 B.3.B.3.49: Food Processing The fonnula M 0.21(loglO a 10glO b) is used in the ...
 B.3.B.3.50: Acoustic Powers The fonnula N = 10glO P is used in radio electronic...
 B.3.B.3.51: HendersonHasselbalch Formnla Doctors use the HendersonHasselbalch...
 B.3.B.3.52: HendersonHasselbalch Formula Refer to the information in the prece...
 B.3.B.3.53: Decibel Formula Use the properties of logarithms to rewrite the dec...
 B.3.B.3.54: Deci.bel Fo~mula In the decibel fonnula D = 10 loglO ( ). the thres...
Solutions for Chapter B.3: Exponential and Logarithmic Functions
Full solutions for Trigonometry
ISBN: 9780495108351
Solutions for Chapter B.3: Exponential and Logarithmic Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter B.3: Exponential and Logarithmic Functions includes 52 full stepbystep solutions. Since 52 problems in chapter B.3: Exponential and Logarithmic Functions have been answered, more than 33758 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Trigonometry, edition: . Trigonometry was written by and is associated to the ISBN: 9780495108351.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

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

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

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

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

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

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

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)ยท(b  Ax) = o.

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

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

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.

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

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

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.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.