log 10x dx log2x -dx Fde 37. 38.

Q: [2 2x log 2x dx

A:

Q: sun(log(1+z)) 230Log(1+ Suin2) um 2-)0 log(i+sinx)

A: We will use the result  If limx→af(x)g(x) = 00 , then limx→af(x)g(x) = limx→af'(x)g'(x)

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: log3 r + [Arcsin(5x)]³ 3

A: To find the derivative of given function.

Q: (log3 (x² + 5)) = %3D dz

A:

Q: 11. log( 2x + 9) + log( x + 3) = log( x² +1) Solve.

A: Logarithm is the inverse function to exponentiation. Logarithm of a number is the a quantity…

Q: log(x³) dx

A: Consider the integral: ∫logx3xdx…

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

A:

Q: 25łn²(x) log (x) dx

A:

Q: log3(x) dx

A: Given integral is ∫ 3x2+log3xdx. Consider u= 3x2.

Q: 4.y=log10 (x4 + 3x² + 1) 5.y = log5 √x² +1 1-x² 6.y-log10 |2–5x3

A: Given 4. y=log10x4+3x2+1 5. y=log5x2+1 6. y=log101-x22-5x3         Derivative of the log functions…

Q: 2 2. + logio x - 3 = 0 10 %3D logx 10

A: 1logx102+log10x2-3=0Apply log rules:2log10x2-3=0Rewrite the equation with log10x=u2u2-3=0u=32,…

Q: 17. log (x² + 3) - log(x + 6)

A:

Q: log(x +1)+log(x −1) = log3

A:

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

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

Q: [32x + log (x) dx = %3D

A:

Q: Solve the equation log(x + 2) + log(x - 1) = 1 algebracially and graphically.

A: To solve the equation: logx+2+logx-1=1 Solution: We know that, logm+logn=logmn Solving the equation.…

Q: log8 square root x/yz2

A:

Q: Solve x +y= logx dx

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Q: Sound in decibels is measured by comparing the sound intensity, I, to a benchmark sound I0 with…

A: Given,

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

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Q: 3 1og, Lx-1)+Log24=5

A:

Q: 5 log x Ans.

A:

Q: sin³ (x)(2x+5)6 Find y' if y = Text=s) log,(2x)' -5

A: We have to find derivative of the given function

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

A:

Q: log5 5^x+y

A:

Q: 1. log(x) +log(x – 1) = log(3x +12) %3D

A: log(a) + log(b)= log(a.b). And, if log(a)= log(b) then a=b.

Q: loga 1 =

A: Given: loga(1)

Q: y=10x log10 X differentiate?

A:

Q: ' log2x dx 62.

A: Given integral, ∫14log2xxdx

Q: y= log2x

A:

Q: In2 log2x dx

A:

Q: Differentiate the function.

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

Q: loga (M/N ) = _________ - ____________ .

A: We know Division property of logarithm is, when we divide two values with same base, we subtract the…

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: 7 + log(16x) = 27 − 3 log(x)

A: Given equation: 7+log16x=27-3logx

Q: 4. y = log(x² – 7) 5. y = ln х+2 x-3 31

A:

Q: dy Example 1: Solve x- +y= logx dx

A:

Q: loga 1 = _______

A: We have to find the value of logarithmic expression: loga1 We know the properties of logarithms,…

Q: 00 dx 2- So V- log x

A:

Q: ® Hing logari thia diffen tiatin, de tormine dy dx y= [at) (xts) Ca5) (x-1)

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

Q: 7 + log(8x) = 28 − 2 log(x)

A:

Q: log 4z a tall var I

A:

Q: ln ex = log1313x

A:

Q: log 7x+2 / 2 (x+6)=0

A: Given

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

A: y=log7xTo differentiate.

Q: 10 log 10 (10x) dx 1 10

A:

Q: log3 (x°. VY16)

A: Given,         log3x9y163

Q: loga Mr = ________________

A: Given expression  logaMr