Simplify the expressions in Exercises 65-68. 65. a. 5log, 7 b. glog, V7 c. 1.3log. 75 d. log4 16 e. log; V3 f. log4 66. a. 2log, 3 b. 10os0(1/2) c. zlos. d. log 121 e. log121 11 f. log3 67. a. 2logax b. 9logя c. log2(en2)(sin x)) c. log,(2"sin ) 68. a. 25log,(3r) b. log, (e")

Q: PROVE that log, 100 = 2(1 +log; 2)

A: We have to prove that                                     log5100=21+log52

Q: Use the definition of logarithm to determine the exact value of each expression in Exercises 1-10.…

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Q: From the equality 10²- - 50 find the value of t by using the equivalent logarithmic form. ±/1+log 50…

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Q: log5 6 is irrational

A: We can prove given result by contradiction method:

Q: single, simplified logarithm Express as a 1- (log510 + 2log53)

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Q: . Show that log(1) = 2nti, n = 0, ±1, ±2, ...

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Q: 6. Use rules of logs to write as the log of a single quantity. a) 2log3 x - log3 4 b) In x + In(x+1)

A: We will use the listed properties of logarithm to solve this question.

Q: In Exercises 9- 16, write each expression as the logarithm of a single expression with coefficient…

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

Q: Simplify the expressions in Exercises 65-68. 65. a. 5logs7 b. 8logavi c. 1.3log 75 d. log, 16 e.…

A: a) 5log57 Apply log rule : alogab=b So we get      5log57=7 d) log416  =log442 Apply log rule :…

Q: For Exercises 25-50, simplify the expression without using a calculator. (See Examples 3-4) 26. log,…

A: We know that, from a logarithmic property, logbam=m·logba           ⋯⋯1logaa=1…

Q: 101. Show that log,(x + V – 1) + log.(x - Vr - 1) = 0.

A: To show: loga(x+x2-1)+loga(x-x2-1)=0 Solution: loga(x+x2-1)+loga(x-x2-1)=0 Considering, Left Hand…

Q: Express as a single logarithm. 5logbt-logb S + logb V - 4 logbu 1) logb 1/2 215 15 v1/2 ) 2) logb…

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Q: Which of the following are equivalent to log, (5)? Choose all that apply. 1 log,(125) 3 O log, (50)…

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Q: jlog(4- ji') (541.5) In log(4ejn) j log(-7)

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Q: In Exercises 10-20, evaluate each expression without using a calculator. If evaluation is not…

A: Given logarithmic expression is: log2 8+log5 25 We have to evaluate it.

Q: Simplify the expressions in Exercises 65-68. 65. a. 5kogs7 c. 1.3loga 75 d. log, 16 e. log, V3 f.…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: 4. Rewrite log(AB²) in terms of logA and logB, or state that this is not possible. log(AB?) = ,

A: We will solve the logarithm problem.

Q: In Exercises 71-78, use common logarithms or natural logarithms and a calculator to evaluate to four…

A: Given: (71).  log5 13 (72).  log6 17 (73).  log14 87.5

Q: What is the value of x in logx > 2log4?

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Q: PROVE that log5 100 = 2(1 + log5 2)

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Q: In Exercises 83-88, let log, 2 = A and log, 3 = C. Write each expression in terms of A and C. 83.…

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Q: Simplify the expressions in Exercises 65-68. 65. a. 5logs? b. glogvi c. 1.3log 75 d. log, 16 e. log,…

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

Q: Rewrite each of the expressions in Exercises 50–52 as thesum, difference, or multiple of logarithms.

A: A logarithm is the power to which a number must be raised in order to get some other number. Example…

Q: Which of the following statements is equivalent to the statement: 16x=65536? log65536(x)=16…

A: Given

Q: For Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as…

A: 25) Given- log47yz To write- The above logarithm expression as a sum or difference of logarithms and…

Q: Prove log, + log, 20 log, 8 = o

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Q: 12. Evaluate, using the laws of logarithms. log, 256 + log, 4 – log, 7+ log, 224 с. 5 d. 6 а. 3 b. 4…

A: 12. Answer:    c. 5 13. Answer:    b. 17/12 log(x) 14. Answer:    d. x = 16

Q: 1 Use log,4 0.712 and log. 12~1.277 to evaluate log, 3 1. log,

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Q: For Exercises 69-78, use log, 2 = 0.356, log, 3 = 0.565, and log, 5 = 0.827 to approximate the value…

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

Q: For Exercises 56-58, use log, 2 - 0.289, log, 3 = 0.458, and log, 5 = 0.671 to approximate the value…

A: given: logb2≈0.289logb3≈0.458logb5≈0.671 we have to find the approximate value of the following…

Q: 93. Use the results of the two exericses above to prove that: (a) log,(÷) = - log, x (b) log,(÷) =…

A: (a) We have to prove that logb1x=-logbx. Consider LHS=logb1x. Use the exponent rule 1am=a-m to…

Q: Express the ratios in Exercises 69 and 70 as ratios of natural loga- rithms and simplify. log,x 69.…

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Q: .Express in index notation: a) loga 8 = c ii. Simplify: 3log3 - log 27

A: I.Express in index notation:  a) loga 8 = cAnswerlogam=n ⇒ m=anThereforeloga8 = c ⇒8=ac

Q: For Exercises 115-126, solve the equation. 10 - 13· 10* 115. 9e = 4 117. (In x) - In x = -4 = 4 116.…

A: The given equation is the exponential equation, hence exponent properties help to solve the…

Q: D.  Express as a single log and natural log :                ( log3 3 +   log3 6 +  log 3 2 ) – (…

A: Consider the given expression: log33+log36+log32-log318 Here, the objective is to express as a…

Q: For Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and…

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Q: Select all that apply: log4 (114) = 11 4log,(11) = 11 O 4log11(11) = 11 O log, (4") = 11 11log,(4) =…

A: Please refer the attached image for complete solution.

Q: 1. Simplify the expression with four a(0,3,4,7,10,12,14).Draw the Circuit in logisim with minimum…

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: Which of the following in not equivalent to log, 3z O 4 log, y - log, 3x O 4 log, y – log, 3 - log,…

A: logmn=logm+logn log(m/n) =logm-logn

Q: 13. Determine whether or not each statement is true or false for all x>0 & y>0; if a false, provide…

A: The solution is :

Q: 13. Determine whether or not each statement is true or false for all x>0 & y> 0; If a statement is…

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Q: Write the expression as a single logarithm with coefficient 1. Assume all variables represent…

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Q: Write as the log of a single quanity: 1/2 [3logx + logy - log5]

A: Given that 12[3logx+logy-log5]simplify it in single log quantity

Q: any positive number can be raised to a power and could therefore be the basis of logarithms.  What…

A: We have to find the logarithm base 4 of 2, 4, 8, 16, 32.

Q: Show that, log(-1+i)² # 2log(-1+i).

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 6. Use log, 10 3.322 and log 8s 0.903 to approximate the value of the expression. log, 100

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Q: Prove that log46 is irrational

A: We have to show that log46 is irrational. We are going to prove this by using contradiction method.…

Q: Prove that log3(25) is irrational.

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Q: Exercise 7. Find the Hoor of each logarithm. That is, jor k being the logarithm, find the inmteger…

A: Please see the below picture for detailed solution.