In Exercises 139–142, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. log, 8 8 140. log(-100) = -2 139. log, 4 141. The domain of f(x) = log, x is (-0∞, ∞). 4 142. log, x is the exponent to which b must be raised to obtain x.

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: 4 Vrite the domain in interval notation of log. ( ), where c > 0. 2-3x,

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Q: 8, Sketch f(x) = log, using 16. properties transformations. of logarithms and

A: Parent function = log2x 1)Negative sign before parent function indicates reflection over x - axis.…

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: log5 6 is irrational

A: We can prove given result by contradiction method:

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

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Q: 105. If f(x) = log, x, show that -f(x) = log1/a X.

A: Given: fx=logax . To show that -fx=log1ax Solution: Property of logarithm states that:…

Q: 120 FIK)T log, =x, express log in terms of x

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Q: 4. Use the properties of logarithms to expand the expression as a sum, differences, and/or cons…

A: The given expression is logbx5b6y7z164 We expand the expression as sum , difference of logarithm…

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: 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: 11. Condense the expression log, (x² – 3x+2) . +2log(x+1).

A: Use base switch rule.

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: Estimate the error in the value log 2.7 obtained from the following dată.

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Q: For Exercises 79-92, write the domain in interval notation. (See Example 9) 82. k(x) = log:(5x + 6)…

A: since we answer only first three sub-parts so we will answer first three. Please resubmit the…

Q: Determine whether the equation log6[4(x + 1)] = log6 4 + log6(x + 1) is true or false. Where…

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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: 1. What is log,, 100? What about log,00 10? 2. What is log, 4? What about log, 2? 3. Express b as a…

A: values=?

Q: log, 12 log, 11 log, 5 log, 27) 2 2 2 2 A) log, V4620 s". 12 C) log, B) log, (12 - s' . 11') D) log,…

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Q: 3(log7(x) + 2 log7(y) − 4 log7(z))

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Q: b). Condense the expression into the log of a single quantity: 3logx + 2logy - logz Ans.

A: Given, The expression 3log x + 2log y -12log z.

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

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Q: Given the function Ax) = logx determine the value of af'(23)- O 1023 23 2.3 230

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Q: Expand log,() o bg(3)-log,(2) O be2)-log-(

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Q: Show that 4 + log 2 3 = 1 + log 2 24

A: Given:4+log2 3=1+log2 24Formula:loga a=1loga ap=ploge a×b=loge a+ logeb

Q: 5log(8)-1 log(x)

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Q: 8. Use the properties of logarithms to expand the expression. (Assume all variables are positive.)…

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: 4. If log,v =logox- (2logby+log,z), what is the value of v?

A: Logarithm s

Q: 1, Section 7.4, Question 047 4 Write the expression log, 7 in the form log, x for b = 7. State the…

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Q: 2log, x-log, y+log, z

A: Follow the procedure given below.

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: 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: Which grows faster In(x) or log (x)

A: ln(x) grows faster than log(x) Look for the graph using Desmos graphing calculator.

Q: The value of a rookie hockey card is modelled by the function = 16log24 x logx³, where x is the…

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Q: In Exercises 117–120, find the exponential model y = aebx that fits the two points. 117. (0, 2), (4,…

A: 118.The exponential model fits the two points 0,2, 5,1

Q: Use the graph of Ax)=4" to estimate the value of log, 27. 50 40 + 30 + 20 10 + -5 4 -3 -2 -ho 1 4.…

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

A: Use property of log

Q: The parent function of h(x) = log3(x) is transformed into j(x) = 2log3(x+3) - 7. Using complete…

A: Given the parent function of hx=log3x is transformed into jx=2log3x+3-7. Using complete sentences,…

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

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Q: Construct the exponential function that contains the points (0, –5) and (4, –80) -

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Q: Estimate using the change of base formula.

A: Consider the logarithmic expression log90.2 to evaluate the value of this, use the change of base…

Q: Let X-N(0,1); show that X member in exponential family.

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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: 4. The expression loga is equivalent to 5 O 3log.y +log, -log,5 O 3logay +2logax – loga5 | Olog (3y)…

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