I expanded log, by writing the radical using a rational exponent and then applying the quotient rule, obtaining log4. log4 x log4 y.

Q: solve for x (use log where is necessary ) 4sqrt(x)=8

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Q: express the following ratios as ratios of natural logarithms and simplify. A) log12 X/log13 X B)…

A: express the following ratios as ratios of natural logarithms and simplify

Q: he logarithmic function f(x) = log x is transformed to g(x) = log(x + 1) + 3. Which of the…

A: solution

Q: If L- k then logL is equal to OA 2109 2log- В. 2(одх - logk) C. 2logx – logk O D. 2logx logk 000

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Q: Given log3 2 = m and log3 5 = n , express in terms of m and/or n.  a) log20 450

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Q: It is defined as the inverse of the exponential function with base b, that is, log,(x) = y - x = b)…

A: Given query is to find the the type of the function and the domain and range.

Q: In x Use the change of base formula loga x = to show that In a log, x = dx x In a d d loga x = dx dx…

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Q: Use the change of base formula to express log, 8 using In, the natural logarithm. Provide your…

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Q: Express the ratios in as ratios of natural logarithmsand simplify. logx a/logx2 a

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Q: Find the inverse 2-Transforrm of log(z f log 241 by Power senies method and by division method

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Q: For f(z) = 3e7'the value of log(f(z)) is

A: Given,       f(z)=3eπ6i

Q: Find the domain of f(x) = log4(x - 5).

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Q: Given y = log x, the base is understood to be Given y = In x, the base is understood to be

A: We know, the common  logarithmic has base 10 ,and is denoted as: log(x). And natural logarithm has…

Q: Use the power rule to expand the logarithmic expression: log(x + 4)2.

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Q: Use the properties of the natural logarithms to simplify the following expressions sin 0 a) In sin e…

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Q: Find the deniva tive of the given Fimction log 4 (x) +16

A: Fx=log4x+16x⇒Fx=lnxln4+16x

Q: The domain for the LOG function does not include which of the following. O 0 negatives O 0 or…

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Q: Evaluate the following without using a calculator (show work!): 6. log1/3 81 7. log36 6

A: 6 Given expression is log1381. We have to evaluate the given expression. Apply log rule,…

Q: Vx*+12 In (x+16)/x-3

A: Given,                   lnx4+123x+16x-3=?

Q: Log with a base "e" (loge) is the same thing as...

A: Given : loge

Q: Find a formula for the inverse of f(x) = -1+ log2 x.

A: Given function is : fx=-1+log2x To find the formula of the inverse.

Q: In the exponential form f(x) = a. bx, the base b can be equal to 1. (A) True (B) False

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Q: Find the domain of f(x) = log4(x + 3).

A: We have to find the domain of logarithmic function: fx=log4x+3 We know that for any logarithmic…

Q: Evaluate the integral. 8 r log 4(x + 8) x +8 xp-

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Q: Use the laws of logarithms to expand and simplify the expression. x3 In Vx (1+x)5,

A: To simplify the expression

Q: Simplify the following into a single logarithm: 4 log(3) - 1 log(z) 4 3 O log 1x O log (4 3 r) O…

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Q: If log m base 2 is x and log n base 2 is y, what is the product mn equal to?

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Q: The unwritten base of log(x) is and the unwritten base for In(x) is

A: Here is the solution

Q: Use the laws of logarithms to expand and simplify the expression. In Vx (1+x)5,

A: We have to express the expression

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

A: Change of base formula:

Q: 6. Find x if the base 7 log of 126 is equal to x.

A: logab = log b / log a

Q: Simplify the following: log 2 x ³-log ₂ x 4 Select one: O a. log ₂x O b. 4 log2X O c. 2log ₂ x O d.…

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Q: write the given in ter ms of 3 to any base log f64 A.

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Q: Since log,(a) = c → a = b°, 1--2 In(즉)- e-1/2. » X = So, y' = 4x(1 + 2 In = 0 when x = -1/2 and y" =…

A: Since logba=c→a=bc                          1=-2lnx5  ⇒-12=lnx5  ⇒e-12=x5⇒5e-12=x⇒        x=5e-12

Q: Let f(x) = logb(3x^2 − 2). For what value of b is f'(1) = 3?

A: Explanation of the solution is given below...

Q: Use the change of base formula to express log, 2 using In, the natural logarithm.

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Q: given log 2=0.3010 and log 3=0.4771, evalute log 6

A: It is given that,

Q: find log(z) where z=-1-3i.

A: Given:      z=−1−3i

Q: 7) use the properties of logarithms to: a, expand the expression log(x3z y2)

A: Consider the given expression log(x3z y2)

Q: Use the Change of Base Formula to evaluate log12 27.

A: log1227

Q: Use the change-of-base formula to find the approximate value. log4 x3 + log2 √x = 8

A: The logarithmic equation is: log4 x3 + log2 √x = 8 We have to solve this equation. We have, log4…

Q: Find the domain of the function. .8 F(x) = log 5x° %3D

A: Given:- f(x) = log5(x8) To find:- Domain of f(x)

Q: In x Use the change of base formula logą x = In a to show that logą x = dx x In a d d loga x = dx dx…

A: Please refer to the image below

Q: State the restriction(s) on the variable x in log(2x-5) – log (4 - x)

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Q: Find log,o x: 10a /0.1 10

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Q: a, logioo[To] b. log 625 C. log 64 d. log Lio01] e. logg! f logm vo 1 log, 2 ho logz 7 t.

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Q: Use the change of base formula logą x = In x to show that In a loga xp x In a d -logą x dx xp In a -…

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