Express the ratios in Exercises 69 and 70 as ratios of natural loga- rithms and simplify. log,x 69. a. log, a log a log2x b. logs x log3x log T0x b. logvx log,b log9x log3x c. 70. a. log, a

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

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Q: Express the ratios in Exercise as ratios of natural logarithms and simplify.

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Q: 15. Write a value in the box below that make the equation true. 1 log, 18 = 2-log, 6 - 4 log, %3D 3

A: Given query is to find the unknown value of the box .

Q: 2. Evaluate, using the laws of logarithms. 2 log, 64 x v64* |+log, 46 43 256

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Let u = In a and v = In b. Write the expression in terms of u and v without using the logarithm…

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Q: 81 a) 3 log16 2 + 2 log16 8 – log16 2 b) log3 6+2 log3 2

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Q: What must logb 1 be equal to?

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Q: The logarithmic function base 10 is called the logarithmic function, and the logarithmic logarithmic…

A: The logarithmic function base 10 is called the ___________ logarithmic functionThe logarithmic base…

Q: Use the definition of common and natural logarithms to simplify. 10log(39)

A: Here given 10log(39) , base of the logarithm used is 10

Q: 4.) 6 log, 41 – 7 log3 27 1 5.) log,+ log24 576 49 6.) log4 100 – log4 50 + log4 64 – log3 27

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Q: 4log 3 - log 33 =

A: Given query is to find the value of the expression.

Q: Which of the following are equivalent to log, (2)? Choose all that apply. O- log, () 1 Olog, (8) O…

A: Let's simplify each expression one by one.

Q: Use these formulas to express the numbers in Exercises 61–66 interms of natural logarithms.61.…

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Q: 95. Use logarithms to prove that for any real number r, (1+)* =e". lim

A: Consider, limx→∞1+rxx=elnlimx→∞1+rxx     ∵elnx=x=elimx→∞ln1+rxx=elimx→∞x·ln1+rx…

Q: use the change- of -base foormula to evaluate the expression as a quotient of natural logs. use a…

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Q: In Exercises 23-25, write each expression as a single logarithm. 23. 8 log, x log, y 24. 7 logs x +…

A: The given expression is 8log7x-13log7y

Q: In Exercises 81–100, evaluate or simplify each expression without using a calculator. 81. log 100…

A: Since you have posted multiple questions so we solve three parts for you, to get the solution of the…

Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning : "I…

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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: 3(log7(x) + 2 log7(y) − 4 log7(z))

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Q: 6. What is the base 4 logarithm of 78 ? *

A: To find the value of log

Q: Let u = In a and v In b. Write the expression in terms of u and v without using the logarithm…

A: We use the multiplication principle of logarithm

Q: Rewrite the expressions in Exercises 5–10 in terms of exponentialsand simplify the results as much…

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

Q: A thermometer reading 65° F is placed in an oven preheated to a constant temperature. Through a…

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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: 8.) log2(3)(37) 9.) log4(64)(37) + log3(343)(2) 2 10.) log10 0.02 + log4– log2 47 3

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Q: Use these formulas to express the numbers in Exercises  interms of natural logarithms.65. sech-1…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Express the ratios in Exercise as ratios of natural logarithms and simplify.

A: We know that, logbx=logxlogblogxn=nlogx We solve the given problems using these results.

Q: Approximate the logarithm using the properties of logarithms, given  logb 2 ≈ 0.3562, logb 3 ≈…

A: Please see the explanation below

Q: Use the definition of common and natural logarithms to simplify. eln(14.125) + 5

A: As it is ln means it is log base e

Q: In Exercises 105-108, evaluate each expression without using a calculator. 105. log:(log, 7) 106.…

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Q: The change-of-base formula states that log, x can be written as a ratio of logarithms with base a as…

A: We have to change the base of the given logarithm  we have,  logbx

Q: Use the Laws of Logarithms to expand the quantity.          ____In  √ab

A: We have to expand ln ab

Q: fin log In () (2)In

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Q: Write out an example of the following: exponent product rule, exponent quotient rule, expo- nent…

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Q: the logarithm of a quotient of two numbers are 0.352182518 and 1.556302501

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Q: log(x) is the exponent to which the base 10 must be raised to get ---Select--- v So we can complete…

A: See below

Q: The number line below shows a value on a log scale. 105 104 103 102 101 100 101 102 10 104 10 What…

A: Given : The above line shows a value on a log scale. What is , approximately , the value of the…

Q: Given that log, a+log, b=3, calculate all the possible integer values of a if b is also an integer…

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Q: Use log,4 s 0.712 and log,5 s 0.827 to evaluate log, 25. 1.54 0.827 0.589 1.654

A: Find the value of log 25 base 7

Q: Define the decibel level B of a sound in terms of the intensity I of the sound and the intensity I0…

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Q: Use the Laws of Logarithms to expand the expression. In √ab

A: Given: The expression lnab. The given expression can be expanded as, lnab=lnab12…

Q: Convert the expression to the log, x using base 10

A: Given that: log5x using base 10.

Q: What are the limits of exponential, logarithmic, and trigonometric functions?

A: Definition and methods help to find the required limit of the given function. A value is said to be…