If f(x) = logx, show that – f(x) log1/a x.

Q: #1 If F(x) = 2 log x and G(x) = x 2 + 3, find G[F(x)]. 2log(x² + 3) (2logx)² + 3 2(x² + 3)logx

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Q: Express in terms of logarithms of x, y, z, or w.

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Q: Express in terms of logarithms of x, y, z, or w.

A: Express in terms of logarithms of x, y, z, or w.  Given expression is log3 y5

Q: Differentiate the function using logarithmic rules. g(x) = ln[x3√(x3+1)]

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Q: determine the nature of functon for even and odd Ax) = log(x+ Vx² +1) ?+1)

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Q: Differentiate the following functions: 1. y = tan(log25x) + x. log3(sec x) 2. logyx = logxy %3D

A: We havey=tanlog2 5x +x.log3 (sec x)Let  u=tanlog2 5x     and    v=x.log3 (sec x)Now y=u+vdiff.…

Q: Determine the maximum and minimum values of the function f(x)= -4 x log2x on the interval [1,4]

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Q: If f(x) = logax, show that ) = -f(x). f %3D

A: Given, f(x)=loga(x) Substituting,x=1x,in f(x) we get: f(x)=loga(x)⇒f(1x)=loga(1x)⇒f(1x)=loga(x-1)…

Q: Express log (x + 1)³ – 2log (x + 1) + 3 log (x – 1)²– log (x³ – 1) as a single logarithm

A: Logarithmic equation: A logarithmic equation is an equation involving the logarithm of an expression…

Q: 4. Differentiate the function. f(x) = log3 (x In x)

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Q: If f(x) = 1- log5 , then f-¹(x) =

A: Given that a function f(x)= 1 - log5x and we find f-1(x) .   Here i attached the solution of this…

Q: Determine whether the equation (log2 x)4 = 4 log2 x is true or false. Where possible, show work to…

A: Given equation log2x4=4log2x. Given statement is false because the identity used is not correct.…

Q: If H(x) = logb 1/x, show that H(b-1/z)= 1/z

A: H(x)=logb1x, we have to show that Hb-1z=1z

Q: Show that loga(√x + √(x - 1)) + loga (√x - √(x - 1) = 0.

A: To show: That logax+x-1+logax-x-1=0. Concept used: Logarithmic product rule: logax·y=logax+logay…

Q: Differentiate the function with respect to x f(x) = 2* · log37*²-4

A: If hx and gx are two differentiable function and fx=hxgx Then f'x=gx×ddxhx+hx×ddxgx

Q: Prove: logaxr = r loga x.

A: Given equation: loga xr=r loga x

Q: Evaluate the limit as x approaches infinity of log7x/log8x

A: We need to evaluate the given limit

Q: Evaluate : |(log x)sin' x dx

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Q: Express in terms of logarithms of x, y, z, or w.

A: The given expression is log3xzy

Q: Express in terms of logarithms of x, y, z, or w.

A: We have to express in terms of logarithms: log4yx We know the property of logarithm,…

Q: Prove that : log 2 xp

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Q: Determine whether the equation, log(x + 9) - log(x + 1) = log(x + 9) / log(x + 1), is true or false.…

A: Given that: The equation is log ( x + 9 ) - log ( x + 1 ) = log ( x+ 9)log ( x+ 1) . Statement :…

Q: Express in terms of logarithms of x, y, z, or w.

A: lnx y4z53 =lnx +ln y4z53 =lnx +ln y4z513  ln y4z513 =13ln y4z5 =13ln y4-ln z5 =134 ln y-5 ln z =4 ln…

Q: In x

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Q: Evaluate : [ vx° +1} log (x + 1) - 6 logx dx.

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Q: If logx^½64 = 3. Find the value of x

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Q: Find the function of the form y log,(x) whose graph is given.

A: Given that: Graph of f(x)

Q: Find the domain of the function. f(x) = 3 - 2 log4 (x/2 - 5)

A: Given function is: f(x) = 3 - 2 log4 (x/2 - 5) We have to find the domain of this function.

Q: Differentiate f (x) = loge (x26")

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Q: Show that loga (x + √(x2 - 1) + loga (x - √(x2 - 1) = 0.

A: To prove: logax+x2-1+logax-x2-1=0

Q: Find the linearization of the natural logarithm f(x)=lnx at x=1.

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Q: differentiate the function f(x)=(x+ log3x)2

A: →Use chain rule of differentiation.→dxndx = n xn-1.→dlogaxdx = 1x logea                        = 1x…

Q: Use the Laws of Logarithms to expand the quantity.

A: Use the Laws of Logarithms to expand the quantity.

Q: Differentiate with respect to the independent variable: f(x)= log base 20 square root x

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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: Differentiate the following logarithmic functions and show that y=ln(x+5)2≠[ln(x+5)]2

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Q: Use the power rule to expand the logarithmic expression: ln √x

A: Given: lnx

Q: Use the power rule to expand the logarithmic expression: ln 3√x

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Q: Differentiate the function below f(x) = log2 (x10ex)

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Q: y = Arccos (logx); y' = * %3D

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Q: solve for x, log(x+5)-log(x+2)=2 please show work.

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Q: function

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Q: Find Log (x In x) Log (x Log x ) dx if

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Q: Differentiate the function. f(x) = log2(1 – 3x) f'(x) =

A: we have to find the derivative of given f(X).

Q: Vx²-1•sin x y%3= %3D (2x+3)4

A: To find: The derivative of y=x2-1·sinx2x+34 using logarithmic function. Formula used: The derivative…

Q: Express in terms of logarithms of x, y, z, or w.

A: Given: log4z3

Q: Differentiate the function y 2x log4(Vx) У' 3

A: Firstly, we use product rule of differentiation which states that (uv)'=u'v+uv'

Q: Use logarithmic differentiaion to evaluate f`(x) f(x) = (5x)^(ln 5x)

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