In Problems 57-70, write each expression as a single logarithm. 57. 3 log, u + 4 logs v 58. 2 log3 u - log3 v 59. log, V - log3 60. log:(-) + log:) 61. log.(x - 1) - 5 log4(x + 1) 62. log (x? + 3x + 2) - 2 log(x + 1) + 2x - 3 2 + 7x + 6 A 63. In(--) + In(**) - In(x² – 1) 64. log( log x + 2 65. 8 log, V3x - 2 - log, + log, 4 x - 4 66. 21 log; Vĩ + log3(9x²) – log3 9 67. 2 log, (5x) 68. log (x° + 1) + log (x² + 1) - log, (2x + 3) 69. 2 log, (x + 1) - log, (x + 3) – log2 (x – 1) 70. 3 log, (3x + 1) – 2 logs (2r – 1) – log5 x

Q: In Problems 43–46, first use appropriate properties of logarithms to rewrite f(x), and then find f'…

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Q: Differentiate log(x² + 1)². O (x2 + 1) ln 10 4x O 4x(x² + 1) ln 10 O 2x(x² + 1) ln 10 4(x2 + 1) In…

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Q: In Problems 19–21, evaluate each expression. Do not use a calculator. 19. log: 20. Ine 21. 2log20.4

A: expressions are given , we have to find its value without use of calculator

Q: 9. 8 logx 4. -2 - 3.

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Q: If log, (4x + 4) = 1, then x = You may enter the exact value or round to 4 decimal places.

A: Find x such that  log24x+4=1,    Apply log property logab=1 if a=b. Therefore, log24x+4=1 when…

Q: 0.004 using a log table

A: The integral part of a common logarithmic is known by, Integer parts as the characteristics and the…

Q: If log, (3x + 3) = 3, then x You may enter the exact value or round to 4 decimal places.

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Q: In Problems 14–19, solve each equation. 14. 5*+2 = 125 15. log(x + 9) = 2 16. 8 - 2e* = 4 17. log(x…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: create 2 sample word problems of integral leading to exponential and logarithmic functions with…

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Q: In Problems 5–7, solve each equation. 5. 3' = 243 6. log,16 = 2 7. logs x = 4

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Q: If you calculate 1 log2 (10!) 1 1 1 + +. log, (10!) + log 10 (10!) with a .. log, (10!) log, (10!)…

A: We will use two properties of Logarithm 1. Change of base 2. Addition of logarithm

Q: In Problems 73-86, use a graphing utility to solve each equation. Express your answer rounde 73.…

A: Given: 1) ln x= -x 2) e-x=ln x

Q: In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as…

A: 37) Given- log525x To write- The above expression as a sum and/or difference of logarithms. Identity…

Q: In Problems 61–74, use a graphing utility to solve each equation. Express your answer rounded to two…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: If log, (3z + 6) = 3, then z = You may enter the exact value or round to 4 decimal places.

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Q: In Problems 26–28, write each expression as a single logarithm. in() + in) - in(c² 1) 1 26. 3 log,…

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

Q: n Problems 25–36, find the exact value of each logarithm without using a calculator. 25. log, 1 26.…

A: As there are multiple questions 25 is solved here.

Q: That half-life of Plutonium-230 is 24,000 years. If 10 grams are present now, about how many years…

A: Consider the equation

Q: 2. Express in terms of sums and differences of logarithms In 2 3x³y (In 2 divided by 3x³y)

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Q: One of your classmates used Chegg.com to solve the equation 3^2x-1= 4^3+x and was given the…

A: Given: 32x-1=43+x

Q: log2x+log2(x+4)=3 x=

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Q: 33. In 8 In Problems 37-56, write ec 37. log, 36x 41. In(ex)

A: Kindly keep a note in step 1️⃣ stating that as per our guidelines we are supposed to answer only 1️⃣…

Q: Suppose that the bacteria in a colony can grow unchecked, by the law of exponential change. The…

A: The colony starts with 1 bacterium and doubles every half-hour.So doubling time of the bacteria =…

Q: In Problems 65–72, the graph of a logarithmic function is given. Match each graph to one of the…

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

Q: In Problems 29-36, suppose that In 2 = a and In 3 = b. Use properties of logarithms to write each…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: In Problems 21-26, graph each function. 21. y = log3 x 23. y = In xns 25. y = log, (-x) 22. y = log4…

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Q: In Problems 63–70, the graph of a logarithmic function is given. Match each graph to one of the…

A: A) The graph of  y=log3x is look like this Point 67 is correct graph

Q: In Problems 13-28, use properties of logarithms to find the exact value of each expression. Do not…

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Q: In Problems 13-28, use properties of logarithms to find the exact value of each expression. Do not…

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

Q: In Problems 75-86, solve each equation. Express irrational solutions in exact form and as a decimal…

A: 75. Given logarithmic equation is: log2x+1-log4x=1 We have to solve for x.

Q: In Problems 25–27, write each expression as a single logarithm. (1 - 2) - ()a + ( 1 25. 3 log4 x? +…

A: We have to write the given expression as a single logarithm: 25.  3 log4x2+12 log4x26.…

Q: Why do you think we need to have restrictions on the variables especially the base (b) and the…

A: Assume a logarithmic function, f(x)=logbx.

Q: 11. If Log(3) = 0.4771 and Log(2)=0.3010, compute Log(√3456) without using a calculator.

A: Given:-log(3)=0.4771log(2)=0.3010using properties of loglog mn=nlogmlogm·n=logm+logn

Q: How are the two equations 102 = 100 and log10 100 = 2 related?

A: Here I am attaching image so that you understand each and every step.

Q: 1. Find x if log,8x

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Q: logaz=5. find loga (1/z).

A: Given: loga(z)=5

Q: If log(x – 3) = log(3x – 9), then æ = DNE

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Q: In Problems 23-26, write each expression as the sum and/or difference of logarithms. Express powers…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

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: 4) Find x: logx = 0 !x:1

A: Log a with base c=b......(logarithm form) a=c^b.....(exponential form)

Q: Solve for x: log x + log(x + 5) = 6

A: Consider the given equation logx+logx+5=6

Q: If log, (4x + 3) = 4, then x = %3D You may enter the exact value or round to 4 decimal places.

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Q: 6. Expand In a*b² as a sum, difference; and/or constant multiple of logarithms.

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Q: Solve for x 5 log(x + 4) = 10

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Q: If log, (5x + 3) = 3, then x = You may enter the exact value or round to 4 decimal places.

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Q: If log, (5x + 3) 3, then x = = You may enter the exact value or round to 4 decimal places. > Next…

A: Find the value of x

Q: Differentiate. 10) y = 7X 11) y = 14-X 12) y = log4(2x)

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Q: Suppose we know that log(x)=7.8. Find the following values. 1. log(10x) 2. log(1000x) 3. log(x/10

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