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

Q: Is ln xy = ln x ln y a valid property of logarithms, where x > 0 and y > 0? Explain

A: ln(xy)=ln(x)+ln(y) using the addition property of logarithm. Where x>0 and y>0.

Q: If log2 X = 5, what is ln X?

A: topic - logarithmic function

Q: Find dx by first using algebraic properties of the natural logarithm (x+7)(x + 8)³ (x + 2)°(x + 3)°…

A:

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

A: Solve the following integral

Q: 1. logx = 2 %3D 2.ln(x + 1) = 5

A:

Q: e-2x 2+x In 3x csc' x -) f(x)=. b)Use logarithm to differentiate: y = (3х-1)

A: a)f(x)=ln(3x)csc2x-x5e-x3f(x)=sin2x. ln(3x)-x5e-x3differentiating w.r.t…

Q: log(x³) dx

A: Consider the integral: ∫logx3xdx…

Q: Which of the following functions grow faster than ln x as x→∞?Which grow at the same rate as ln x?…

A: Let f(x) = ln x) and g(x) = e-x Let f(x) and g(x) be positive for x sufficiently large,  a) f(x)…

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

A:

Q: How is the logarithmic function y = log a x defined?

A: To define the given logarithmic function.

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

A: topic - logarithmic equations

Q: Which of the following functions grow faster than ln x as x→∞?Which grow at the same rate as ln x?…

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Q: Find the domain of the logarithmic function f(x) = ln(x - 1)2.

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: y = (cos(x²))* -2 Co:

A:

Q: Find the deri vative OF +he exponential function: y = arcsin e*

A: Given function - y = sin-1e-xDifferentiating on both sides with respect to x - dydx =…

Q: d Find (3"). Type In(x) for the natural logarithmic dx function.

A: we have to find the derivative of 3x

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

A: Given that

Q: dy Use the properties of logarithms to help perform dx COs x y = ln 3 – 5x2 - dy dx ||

A: As we know that ddxlnx=1x

Q: 'x + 2 3. -dx x + 1

A: To integrate: ∫x+2x+1dx Solution: Evaluating the integral.…

Q: y = log (esin =)

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Q: Solve the logarithmic equation for x. In( x - 1/2) + In 2= 2 In x

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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: Determine y′(x) if y(x)=(4x^3+6)^sinx.  Enter an exact answer in terms of a natural logarithm.

A:

Q: 3 log25 x = 2

A: It is logarithms problem.

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

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Q: cos e Differentiate y =- using Logarithmic differentitation. nxV2x +1

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Q: 1.Solve by logarithmic differentiation -(x+1)(x+2)(x+3)2 Y=In(- V(x+3)3 (x+4)*

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Q: Find dy/dx if y=log(-4x^2+2)

A: To find the dy/dx of the given function.

Q: express the following as a single logarithm ln x+ a ln y - b ln z

A:

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

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Q: dy Find by first using algebraic properties of the natural logarithm dx (x+ 4)(x + 5)° In function…

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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)?…

A:

Q: find the deliva tiva dy for the function by using logarithmic

A: Derivative.

Q: Differentiate. y =9* . log 7x (g*. log 7×) • log 7× dx

A:

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: Differentiate the function.

A: Given: y=2xlog10x To Find: Differentiate the given function. Concept: i. Product…

Q: Differentiate. y = log 4X d. dx 1og 4x =

A:

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

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Q: Differentiate. y = 12* • log 6x d x (12*- log ex) = D 6x) = [ %3D dx

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Q: se logrithmic differentiation. y=(sqrtx)^7x

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Q: Solve the logarithmic equation for x. log x + log(x - 1) = log(4x)

A: Consider the provided equation, logx+logx-1=log4x Solve the logarithmic equation for x. Apply the…

Q: Solve the logarithmic equation for log x + log(x–1) = log(4x)

A: Given, log(x)+log(x-1)=log(4x) By applying the log rule, loga+logb=logab ⇒log x(x-1)=log…

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

A:

Q: Solve the logarithmic equation for x. 2 log x = log 2 + log(3x - 4)

A: Given 2 log x = log 2 + log(3x - 4)

Q: Solve the logarithmic equation for t. ln(at + b) = c if a ≠ 0

A: To solve the given logarithmic equation.

Q: Just as exponential functions are distinguished by their rapid rate of increase, the logarithm…

A: Consider the graph:

Q: ` log x dx

A:

Q: Differentiate. y= log 7x dx log 7x=

A: y=log7xTo differentiate.