The logarithmic expressi on In can be rewritten as (1) 3ln y- 2 In y- 6 (3) 2 1-6 In y (2) 2 (4) Vin y – 3

Q: ,2,3 Expand into several logarithms: x'y In 25

A: Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to…

Q: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

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: How do I expand this log expression? xz/5y x times the square root z over 5y

A: We have to expand the log expression:

Q: The logarithmic function f1x2  ln1x  12 has theasymptote x

A: Given f(x)=ln(x-1)

Q: let f(x)= x^5x where x>0. use logarithmic differentiaiton to find f'(x)

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Q: Express x in term of y if: log,xy =2 +2log,x -3log,y

A: Given that:  log4xy=2+2log4x-3log4y We have to express x in the form of y.

Q: Find if z = log2 y – 6 log5 y. dy dz dz In- dy y In 10 dy y ln 10 Option 1 Option 4 64 dz In- 64 dz…

A: We know, ddxlogax = 1x·ln a a·ln b = ln ba ln a - ln b = ln ab

Q: 8. If logax = loga6, then x = M 9. logaN In 8 10. True or False. = 2. In 4

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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: 2. The function f(x) = log, x is the logarithm function %3D So f(9) = -- f()- with base %3D f(1) =…

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Q: If x2 + y2 = 25xy . Then prove that 2 log(x+y) = 3log3 +logx + logy

A: It is given that x2+y2=25xy add 2xy to both sides  x2+y2+2xy=25xy+2xy using the formula…

Q: snip

A: The exponential function and the logarithmic function is strictly increasing functions for x > 0.…

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: 2. Differentiate: a) y = log2(3x) %3D 2 b) f(x) = –7 log(x²) %3D

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Q: If k is a positive constant, show that x^2 e^-kx approaches 0 as x --> ∞.

A: Given  The x2e-kx approaches 0 as x→∞.Where k is a positive constant .

Q: (22x + 2) dx 11 In|x² +4] +2 tan -1 x2 + 4 +C 2 Logarithm function is missing parentheses around its…

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

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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 y by logarithmic differentiation. y=x²X A O y = 2 In x+2 2 In x-2B O y = x²* (2 In x+2) .C O y…

A: Use log to differentiate

Q: dy : Prove that dx or ỹ for expression y log2(x²) is equal to ỹ = 2[1-log2 x² In 2] %3| x2 x³ In 2

A: Given, y = log2x2x2    We have to prove dydx or y¯ = 21-log2x2.ln2x3ln2

Q: Prove: logaxr = r loga x.

A: Given equation: loga xr=r loga x

Q: 2. Expand the following natural logarithms: In(zx'y") b. In- zy а.

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Q: Determine if the given functions are LI or LD by computing the Wronskian : -2x Yi = e*,y2 = e*,y; =…

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Q: Show that J log(1 + tan0)d= log2

A: Given that: To prove:        ∫0π4log(1+tanθ)dθ=π4.log2

Q: write the logarithmic equations in exponential form.

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

Q: Find the exponential functions of the form f(x) ab* that pass througl

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Q: The derivative of f(z) = Log(2iz – 4 + 6i) at z = -3 + i is O Undefined. O Log(-6). O None of them O…

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Q: Evaluate loge 7 by Simpson's (i) rd, and (ii) th rules.

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Q: Combine into a single logarithm. In(x – y) – 2 In(x² + y²) OIn (x-y)3 In (x²+y²)* In Va-y) (x²–y²)?…

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

A: log (a.b) = log (a) + log (b) log (an)= n.log(a)

Q: 4. The expression log(sinx) – log(cos.x) , 0<x<, is equal to A. log(sin x cos x)

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Q: II. Determine the derivative of the ff. logarithmic functions 1. y = 25 In 5x 2. y = -10 In 3x4 3. у…

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Q: 7. Use properties of logarithm to expand In (y³z²Vx – 1)

A: Property of logarithm

Q: Solution to the equation Log(2iz + 1) = in is None of them z = ni z = i

A: Usually, log x is represented as log10x . If log x=y , then x=10y .  The natural logarithm, ln x is…

Q: Determine the maximum and minimum values of the function f(x)=-4 •log 2x on the interval [1,4]

A: Given function is  on interval [1, 4].

Q: Evaluate y for the fx)= 4"-5 log,(x) 4*ln 4- Inx 4- x In 9 4- In 9 4'ln 4- x In 9

A: Answer

Q: 4. Express the following single logarithm: as a i) log3 54 -log3 6 ii) 2 In (5a’b) – In (125 aº b²)…

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Q: (b) Show that 1 1+ 2 tanh- (2) = ; log

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Q: 2 log(x+y) = 3log3 +logx + logy

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Q: 6) If u = log (x² + y²), then prove that log (x² CSScanned with CamScanner dydx ôxôy

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Q: 5. Prove if the following function is differentiable y = x loge-*

A: Given that: y=xloge-x

Q: 2. Evaluate [log(-1-/)(-2- j2)] tan(4 + 3i) cosh-1

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Q: d log, x = 1 dx [(In a)(x)]

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

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

Q: 4. Show that sinh-1 x = log(x + vx² + 1).

A: We have to prove the result.

Q: Evaluate So ·∙log 1+ax 1-ax (: ( dx x√√1-x²

A: A very good problem. This problem illustrates the power of differentiating under the integral sign.…

Q: 1. Find for the following functions : dx 2x (ans.: 3x' log,( 3 – 2x)-’ (3–2x )In 2 45) y=x' log,(3–…

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