If H(x) = log, 1/x, show that H(blz) = 1/z.

Q: Suppose that log, x = 5 and log, y = 4 compute %3| log, Vx²y³

A: Given

Q: Use the trapezoidal rule with five function values, together with appropriate log laws, to show that…

A:

Q: Find y' for y = (2(x^2+1))/(x(sqrtx+1)) using logarithmic differentiation

A:

Q: Find the integral: log7 X dx = %3D

A: Solve the following integral

Q: dy Find using logarithmic differentiation if y = (3x)2". dæ

A:

Q: solve: loga (4x+4)= log₂ (-7x+19) = X= AS lenter DNE if no rolution)

A: topic - logarithmic equations

Q: Differentiate the following functions using logarithmic differentiation. 1. y = (2x + 1)š(3x – 4)

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

Q: )For x>0, xER, find the 0() estimate of order of the function 6x* + 3x logx - 5x3 + 7x-9 *(x) = 3x3…

A: Given: 6x4+3x6logx-5x3+7x-93x3+2x2logx2-5x x>0, x∈ℝ

Q: dz dz +y дх = 50 +x4°y+y5° ), Prove that x ду If z= log (x50

A:

Q: If ƒ(x) = (7x − 2)² · (8x² + 8)ª, find ƒ'(x) using logarithmic differentiation

A:

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: Find using logarithmic differentiation if y = (2z). dr %3D

A:

Q: Find the derivative of the logarithmic function. 6 + y = In

A:

Q: Show that log, (Vx + Vx – 1) + log.(Vx – Vx – 1) = 0.

A: To show that logax+x-1+logax-x-1=0. Solution: We know that, logm+logn=logmn Simplifying the left…

Q: dy Find using logarithmic differentiation if y = (2x)2". dr

A:

Q: Differentiate. y= 11* . log 7x dx (11*. log 7x) =O

A: Given that

Q: Differentiate with respect to x:* y = log, (x) :() 2+ In x - In x Option 2 Option 3 2 - In x 1+ In x…

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

Q: Find the derivative of the function y = log4 (6x + 1)

A: Given information: y=log46x+1 Log rule: logab=lnblna

Q: Differentiate implicitly to find y' log3 (x). tan cy+ 1) = y2 %3D

A:

Q: )=1/x. Using this, compute the

A:

Q: f(x) = (a

A: Here, let y=f(x)=x3x3ex3 Taking natural log (ln) on both sides: ln y=lnx3x3ex3⇒ln y=lnx3x3+ln ex3⇒ln…

Q: y = log (4x°)

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

Q: Differentiate the function Y = logi5(x° +1)

A: Differentiation of logax is defined as dlogaxdx=1xloga Chain rule of differentiation states that…

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

A:

Q: Find the exact x-coordinate where there is a horizontal tangent line to the graph of f(x) = x10°.…

A: Given,          The function is fx=x10x.

Q: dy Find dz using logarithmic differentiation if y = (3x)3.

A:

Q: Prove that : log 2 xp

A:

Q: Find d/dx(2x) Type ln(x) for the natural logarithmic function.

A: Given query is to find the derivative of 2x.

Q: dx Evaluate log - 1+ax 1-ах

A:

Q: The third derivative of the function is y = log 2x3

A: We can find the answer as below

Q: y = log,(4x - 8x)

A:

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

A:

Q: find dy if by using logarithmic

A:

Q: Use the technique of log differentiation to find when y = (sin(x))In(x) %3D dx and then evaluate it…

A: Given that y=sinxlnx find dydx using log differentiation

Q: Determine the approximate values af log3 (VI6,0L + V24.99 (Instruction d logax dx In a

A:

Q: A Disguised Form of the log Rule, Find

A:

Q: (т3 + 5) e2x /2x – 1

A:

Q: Q5 Answer with all details, By using Logarithmic find the 3 x(x-2)sinx derivative of y = (x2+1)Vsecx

A:

Q: =) Express the new function h(x) log2 in terms of the original function f (x) log, (x).

A:

Q: If y = loge(sin x)? dx will be equal to dy

A: Given: y=logesinx. To find: dxdy Solution: Chain rule of differentiation states that:…

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

A:

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

A:

Q: 3. Find the derivative of (x² + 3) (3x – 3)² Y = Vrez+1 Hint: Use logarithmic differentiation!

A:

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

A:

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: ` log x dx

A:

Q: Find of, af , for f(x, y) = log₂ (3г² - +y)

A: Solution of given question is written in below steps.

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'