In Exercises 74-79, solve each logarithmic equation. 74. log.(3x – 5) = 3 75. 3 + 4 In(2xr) = 15 76. log,(x + 3) + log,(x – 3) = 4 77. log:(x – 1) – log:(x + 2) = 2 78. In(x + 4) – In(x + 1) = In x 79. log,(2x + 1) = log,(x – 3) + log,(x + 5)

Q: Show that loga 12x + 2x - 12 + loga 12x - 2x - 12 = 0.

A: given :                      loga (12x+2x-12) + loga(12x-2x-12) = 0 The product rule for logarithms…

Q: Write the equation in its equivalent exponential form. 3 log7343 What is the equivalent exponential…

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Q: How are the two equations 102=100102=100nn and [][]log10(100)=2log10⁡(100)=2 related?

A: We need to show relation between given equation.

Q: 5. Solve: x4-log2 x = 16 %3D

A: To solve the following equation.x4-log2 x=16

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

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Q: In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in…

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Q: Evaluate the expression log ∛10 without using a calculator. If evaluation is not possible, state the…

A: Known facts: logab=bloga log10=1

Q: Exercises 150-152 will help you prepare for the material covered in the next section. In each…

A: log232On simplifying further we get:log232=log225        (using,25=32)⇒log232=5log22…

Q: Evaluate the expression log4 64 without using a calculator. If evaluation is not possible, state the…

A: Given expression is: log464 In logarithmic function we know that:…

Q: For Exercises 53-55, write the logarithmic expression as a single logarithm with coefficient 1, and…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Use the Laws of Logarithms to combine the expression. 3 In(2) + 5 In(x) - - In(x + 7)

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Q: Write logarithmic equation in exponential form. 3 = log5125

A: Given- 3=log5125 To write- logarithmic equation in exponential form. Identity Used-  lognnq=qlognn…

Q: An exponential function in the form y = 729(b)* contains the point (3, 1). What is the value of b?

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Q: Evaluate the expression, log3(-9) without using a calculator. If evaluation is not possible, state…

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

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Q: Using logarithmic properties, what is the solution to log4(y – 9) + log43 = log481? Show all…

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

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Q: Evaluate the expression log3 38 without using a calculator. If evaluation is not possible, state the…

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Q: In Exercises 93-102, solve each equation. 93. 52. 54r = 125 94. 3+2.3 = 81 95. 2|ln x| – 6 = 0 97.…

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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: a) In x-3VIn x +2=0 giving answer in exact form and decimal approximation to 3 decimal places

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Q: In Exercises 44–46, use inverse properties of logarithms to simplify each expression. 44. In e 45.…

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Q: What is the real part of Log(-5 + 51)²? What is the value of Log(-5+ 54)? – 2Log(-5+54)?

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Q: ( 3vx log9 x²+9,

A: The expression is  log9 3xx2+9

Q: In Exercises 50-53, use properties of logarithms to expand each logarithmic expression as much as…

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Q: Express in terms of logarithms without exponents. logb(x3y9z) What is the equivalent expression?…

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Q: Evaluate the expression log3(log8 8) without using a calculator. If evaluation is not possible,…

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Q: Is it possible for a logarithmic function to have a domain of (-∞,4)? Why or why not? Include an…

A: We have to find a log function which domain is (-∞,4)

Q: Express th equation in exponential form.

A: Part (a) - log381 = 481 = 34                                If logba = c, then a = bcHence,34 = 81

Q: Use the Laws of Logarithms to expand the expression. In(/ x5 + 6

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Q: 15 log 9

A: Use the following logarithmic properties:…

Q: Expand the logarithm fully using the properties of logs. Express the final answer in terms of log æ.…

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Q: I estimate that log8 16 lies between 1 and 2 because 81 = 8 and 82 = 64.Determine whether the…

A: Given information: The value of log816 lies between 1 and 2, because 81 = 8 and 82 = 64.

Q: Solve: log21(x-84)=3-log21x

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Q: Solve. 5) log4 (9x - 7) = 1 5)

A: logb (x)=y exactly if  by =x and x>0  b >0

Q: Evaluate the expression log100 0.1 without using a calculator. If evaluation is not possible, state…

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Q: .162,8 Write expression log as a sum or z16 difference of logarithms with no exponents. Simplify…

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Q: What can you conclude about log3 81, or log3 92?

A: Our aim is to find the conclusion between log381,log392

Q: In 2 log2x

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

Q: Write logarithmic equation in exponential form. log 0.001 = -3

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Q: In Exercises 41–67, use properties of logarithms to condense each logarithmic expression. Write the…

A: Note: We will answer the first question. Please specify the one you would like answered.

Q: Evaluate the expression log16 4 without using a calculator. If evaluation is not possible, state the…

A: Evaluate: log16 4

Q: 2. How many 3-letter words with or without meaning, can be formed out of the letters of the word,…

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Q: Evaluate the expression log3(log2 1/8) without using a calculator. If evaluation is not possible,…

A: Evaluate the expression log3(log2 1/8) without using a calculator. If the evaluation is not…

Q: In Exercises 29-44, write each expression as a logarithm of a single numbe if possible. Assume each…

A: We have to express in single expression from the given expression

Q: Use properties of logarithms to expand the logarithmic expression logb(√xy3/z3) as much as possible.…

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Q: 9. Use common logarithms to approximate log, 72 to four decimal places.

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Q: log, n - Glog, m – log, n) as a single logarithm. 4 1. Express- log, m + logx n) as a single…

A: We have to convert the following into a simple logarithm form -  34logxm + 23logxn - 12logxm -…

Q: 2) Use laws of logarithms to fully expand the expression. log9 x²+9.

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Q: Use the Laws of Logarithms to combine the expression. 5 In(2) + 2 In(x) -- In(x + 7) 2

A: Using laws of logarithm to simplify given expression.