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

Q: Given that log x= 4 and log y = 1.5 , find the value of log (x²y)

A:

Q: Use the fact that d lIn x/dx = 1/x, as well as the change-of-base theorem for logarithms, to prove…

A: Given: prove that ddxlogax=1xlna We know that logpq=lnqlnp…

Q: Assume that for some base a, logąx = 0.3000, logay = 2.8642, and logąz = 1.7642. Find %3D %3D loga…

A: log (mn)= log(m)+log(n)logmn=log(m)-log(n)logam=m log (a)

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

A:

Q: x] is a O log 2

A:

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

A: Solve the following integral

Q: H.w find the root fcx)= X log x-loo when [ !,3} by Bisaction ?

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Solve: x a + y = logxsin(logx). dx

A:

Q: What is the zero o of the funcHon Y= loge (x+G)-I?

A: Given: The function, y=logxx+6-1.

Q: Find the equation of the vertical asymptote f(x)=log(x+5)

A:

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: The loudness (x), measured in decibels (dB), of a sound of intensity x, measured in watts per square…

A: Given,            L(x) = log xI0  where  I0 = 10-12

Q: y = v4x + 3 log2(x² + 2)

A: Given query is to find the derivative of the expression.

Q: Differentiate the function. f(x) = log13(xe*) %3D

A:

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

A:

Q: Find the equation of the vertical asymptote f(x) = log(x + 5)

A:

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

A:

Q: Use the properties of logarithms to simplify the following functions before computing f 1x2.

A: Given expression: fx=lnsec4x tan2x

Q: y = ln √4x² (Hint: Apply first a property of LOG.)

A: Let's find first derivative.

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

A:

Q: Rearrange this equation to isolate A. H = K + log () A =

A: we have to rearrange the equation to isolate A

Q: Given that logp q = x 2 and logq p = 1 2x−1 , find x

A:

Q: Given that log x = 3 and log y = 4, find log Vx3y2. O 6.93

A: Using the properties of logarithm we expand it

Q: y=x^logv5(x) dy/dx=?

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: What is h′(x) when h(x)=log 7 (8x+4 / x 6 7 x)?

A: Consider the function

Q: Evaluate: dx (x+1) log(x+1)

A:

Q: If f(z) = 10", find f(log 2).

A:

Q: Differentiate (a) f(x) = 43 x and (b) f(x) = log2(x 2 + 1).

A: We have to differentiate the given function    the given function is    (a) f(x) = 43x   (b) f(x)…

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

A:

Q: = log z in the regio

A:

Q: Find dg Using Logarithmic differentation y =3 2x +1

A:

Q: (а) е" =D1 %3D (b) log(x – 3) + log(x - 6) =

A: Given that: (a)ex2-9=1(b)log(x-3)+log(x-6)=1

Q: Differentiate the function.

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

Q: Expand the logarithimic expression.

A: Let the given logarithmic function be y - y = log2xx2+1y = log2x+log2x2+1…

Q: dy Find , given y = log3 dx 10- x 2x5

A: Given y=log310-x2x5⇒y=log3e · loge10-x2x5      Using the property: logab=logac·logcb

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

A:

Q: Use the defination of the logarithmic function to find x.

A: Given: log x=3 log e2=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: Differentiate. y = log , (x° + x) d log 4 (x° +x) = [O

A: Given function is: y=log4x8+x As per logarithmic rule: logab=logbloga So: y=logx8+xlog4

Q: ` log x dx

A:

Q: Use log, 3 z 0.5869 and log, 5 z 0.8598 to find an approximate value for V5 logb 9

A:

Q: Find dy dx given (х* + 3x — 1)° /1 – 3x³ y , by using property of logarithms.

A:

Q: Find for the following function: 3- y = log,(x - x) 4- y = In2

A: It is an important part of statistics . It is widely used .