) Find the value of log. ) + logal). + log. (). Show work. your

Q: 7. If log 3 (log a + log b), show that a? + b² – 7ab = 0.

A:

Q: ,11,,6 The expression log can be written in the form 23 A log(x) + Blog(y) + C log(2) where A = В -…

A:

Q: 5. A logarithm is best defined by which of the following words:

A: A logarithm can be defined as the exponent that indicates the power to which a base number is raised…

Q: a. log i'

A:

Q: 3. (a) 53  125, so log (b) log5 25  2, so

A: Given:            (a) 53=125(b) log5 25=2 (a)     53=125 By definition:       bc=a⇔logba=c So,…

Q: Prove that the number log, 13 is irrational. Recall that log, a = x means that bª = a.

A:

Q: Express the indicated logarithm in terms of ?, ? and ? with the assumptions that log 2 = ?, log 3 =…

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Q: 23. Given that p log, 5, q= log, 2 express the following in terms of p and/or q. 23) log , 250…

A: The solution of given problem is followed by

Q: Show that loga b logb a= I for all a, b > 0 such that a # 1 andb #1.

A: We will use the change of base formula

Q: 1. Which of the following statements is TRUE? O log, z ee (la a) O log, z = In(et. •) Ina log, z Inz…

A:

Q: 12. Find r, where log2(ar) – log,(3 – r) = log,(r), and 0 < a < 3. %3D

A:

Q: Show that loga aMN b = loga M - loga N, where a, M, and N are positive real numbers and a ≠ 1.

A: We have to prove, logaMN=logaM-logaN Let us consider that, M=ax⇒x=logaM          ⋯⋯1N=ay⇒y=logaN…

Q: If log, 3 = 0.7925, log, 5 = 1.161, and log, 7 = 1.4037, then the value of log, V21 is O 2.2767 O…

A: Given: logb3=0.7925 logb5=5.161 logb7=1.4037

Q: = d. Find an expression for = c and log,(2) log, (50) in terms of c and d, but not involving…

A:

Q: ´M` Show that loga N log, M – log, N, where a, M,and N

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Q: Find a formula for the exponential function of the form f(x) = a· bª that passes through the points…

A:

Q: 50. If log, x= 4 and log, y=5, then evaluate the following. a) log, r'y b) log. ay

A: We can solve the problem by property of logarithm.

Q: Suppose that, for a certain real number b > 0, log,(3) = 2.53 and log,(5) = 4.21 Find log,(45) 1…

A: Given:  logb3=2.53   and logb5=4.211) logb45=logb9×5we know that log(ab)=loga +logbThen…

Q: 2. Which of the following is equivalent to the expression: 2+3 log, (z+ 1) – log (2z – 1)? 2(z + 1)*…

A: This is very complicated problem.We have to think deeply to solve this problem.Therefore I can solve…

Q: Find the largest value of z that satisfies: loga (z) – log,(z + 3) = 8 %3D

A:

Q: 3. Given that log,x = 2 and that log, y = 3, use the logarithm laws to expand the following and…

A: \Logarithm rules:logaxy=logax+logaylogaxy=logax -loga yloga x4 =y loga xlogaa =1

Q: snip

A: Prove that: logaMN=logaM-logaN, where a, M and N are positive real numbers and a≠1

Q: 5. Evaluate the following using a method of your choice. a. log,729 = b. log 7776– log,36

A:

Q: Show that loga(M/N) = loga M - loga N, where a, M, and N are positive real numbers and a ≠ 1.

A: Here given equation loga(M/N) = loga M - loga N

Q: log(2,5,) -log(=, ) – log(2,) ylgn O İhi O

A: The detailed solution is as follows below:

Q: 2) Choose the best answer. If log, 2 0.69 and log, 8 = 2.08, then log, 4 = %3D %3D 1.38 O 1.39 0.36…

A:

Q: 3. (a) 5 = 125, so log (b) log, 25 = 2, so

A: a. 53=125 b. log525=2

Q: 10. Given that ļlog, 2= 0.301, log, 7=0.845, and loga 11 = 1.041, find the following, if possible.…

A:

Q: log 30.477 and log,5x 0.699. Use these values to evaluate log, 75. log 75= %3D

A:

Q: Find the real number æ such that x log, 3 = log10 3. (Hint: Let a = log, 3, and use this.)

A: we have xlog2(3)=log10(3)

Q: ,15 The expression log can be written in the form z18 A log(x) + Blog(y) + C log(z) where A = В -…

A: Given logx11y15z18We know that log(AB)=log(A)+log(B)and log(AB)=log(A)-log(B)Therefore the…

Q: Given that x, y, z >1 and w be a positive number such that log, w = 24, log, w = 40 and logrvz W =…

A:

Q: 27a b² Evaluate log, (- V81cd whenever log, (a) = 4, log3 (b) = 0, log, (c) = -1, and %| log3 (d) =…

A:

Q: 3. If log, 3 = $ and log, 5 = #, rewrite the following expressions in terms of $'s and #'s. a. log,…

A:

Q: Show that loga ( 1/N) = - loga N, where a and N are positive real numbers and a ≠ 1.

A: To Show: loga1N=-logaN, where a and N are positive real number and a≠1. Concept: i.…

Q: 7. Use log, 2 0.4307 and log, 3 0.6826 to approximate the value of log, 12. O A. 1.5440 O B. 0.8681…

A:

Q: uv uw log- + log- + log– – log(uvw) W

A: Given,            loguvw+ loguwv+ logvwu -  loguvw

Q: 3. Use log, 2 0.4307 and log, 3 0.6826to approximate the value of log, 54. A. 0.8820 B. 2.4785 C.…

A:

Q: 2. Given p = 2' and q = 2', express log, p'q in r and t terms. 64

A: Given

Q: 2. Use the laws of logariths to express each as a logardh eg a Single expouscion a. log a + log, b +…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Simplify sinnh(loge(4)). Express ecos(3+iloge(4)  in the Cartesian form.

A: The given problem is to evaluate and simplify the given complex expressions and express in the…

Q: 5. Which of the following expressions is equivalent to log(3) - 2 log(2x) + 3 log(y) 3y5 4x2 3y6 log…

A: log3-2 log2x+3 logy2

Q: 2. Prove the following equations: A. HOg, 6 = 1 logab a 1+log, b B. log1 a? = -2

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Q: 1. Evaluate without using a calculator. Show steps. a) log,÷+ og, 100 b) og , 27 – log,5

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Q: Which of the following statements is false? O log3 9 = 2 because 32 = 9 %3D O log, 0 does not extist…

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Q: If log, 4 = 1.39 and log, 3 = 1.10, then log, 12 = %3D 4.17 4.40 2.49 O 1.529 0.29

A:

Q: A) Given that x= log, 5 and y=log, 2 log, 60 in terms of x and y. , rewrite

A: A) Given that x=log35 and y=log32   To Calculate: log360 in terms of x and y.   Note: As multiple…

Q: 9) Evaluate log. Use log x = 2, log y = 6, and log z = 12.

A: