log/ yx-y+3 1-4xt y 4X - log 3 4x ニ

Q: 1) 2-log₂ y = 2log₂ (x+y) log₂ (x+y)+ log₂ (x² − xy + y²)=1

A: We have to solve given problems:

Q: The graph of a logarithmic function is given.Match each graph to one of the following function

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Q: (log3 (x² + 5)) = %3D dz

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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: Differentiate. a) y=log2(3x) b) f(x)= -7 log(x2) c) g(x)= x6log(-4x) d) h(x)= log8(2x4-3x)

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 9) logx-1(4x – 4) = 2

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Q: 4) f(x) = log14 × %3D

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Q: 4x³ (log3 x)" (csc5 x) Vsinh(2x – 8) b. y =

A: We differentiate the given function using quotient rule of Differentiation i . e .  If   y ( x  ) =…

Q: 7. f(x) = 6e* + log2(7x² + 3x + 1) f'(x) =

A: Given: fx=6ex+log27x2+3x+1 Differentiating fx with respect to x, f'x=ddx6ex+log27x2+3x+1…

Q: 25łn²(x) log (x) dx

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Q: log 3 (x + 1) + log (y – 2) = 2 log3 (y) – log3 (r + 1) = 0

A: Given equation - log3(x+1) + log3(y-2) = 2log3x+1y-2 = 2                            log(a×b) =…

Q: logzx = 3 – log,2x 7. In(x + 2) + In x = In(x+ 12) Pgol+x0ol 6. log 3x + log 2x = log 150 %3D 8.…

A: As per the company's guidelines, we are supposed to solve the first three sub-parts for you, kindly…

Q: 3x = 76x-5 d. log2(x+30) + log2x = 6 e. 2x^2 = 162x-3

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Q: (8) y = x³ log3x, find y' %3D

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Q: X-y 19. If log 3 (logx + logy), show that x+y = 11r %3D

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Q: i) log, (5x + 4) – log,(4x) = 2. ii) 9e* + 4e-x – 12 = 0.

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Q: * (x-9) log2 y

A: Since, you have asked multiple questions in a single request, we would be answering only the first…

Q: Log1/2 4=x

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Q: 1) x³+ 2x - 2y = x² logx + x dx3

A: Since you've asked multiple questions, as per the answering guidelines we are supposed to answer the…

Q: Equation n(2-x) = 3 %3D b) log2(x) + log2(x - 7) = 3 c) log(x) – log(x - 1) = log(4x) %3D

A: ln(2-x) = 3(2-x) = e32-x =20.12-20.1 = x x = -18.1

Q: [ Зх +1 x – 3 A 3x + log (x- 3) 3x + 10log (x- 3) в Зх + log. (x- 3) +с 3x + 10log (x – 3) + c

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Q: x² 6 + ,X log (x² + 7)(x³ – 5)² -

A: Laws of Logarithm:

Q: 4 log, (x) – log, (x² – 2x) Condense

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Q: Approximate x to three significant figures .

A: x=log 8.4 , b. log x=-2.4260 c. ln x=1.8

Q: log2(x+1)-log2(2-x)=3

A: Given that:   log2(x+1)-log2(2-x)=3NOTE:  First expression has two values.So need to be corrected.

Q: 7. log;(x²) =, x log5(_ 8. log,(y*) = x log-(. 9. log(V1000) = – x log( %3D

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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: Solve the equation.

A: log57x=2+logx-2

Q: log, (x + 1) = 2 + log, (3x – 2)

A: We have to solve the equation: log4x+1=2+log43x-2 We know the properties of logarithm,…

Q: y = log, (2a – 1) · (x³ – 4x)

A: Given: y=log42x-1·x3-4x Formula used: Product rule: f·g'=f'·g+f·g' Constant multiple rules of…

Q: 3.) y = log, - 6·x³ -6.x³ y' = %3D

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Q: Solve the system

A: The system is given as logx2=y+3 .…

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: 3. 2 log x< log (2x-1)

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Q: Differentiate.

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Q: 1. log3(2x – 1) > log3 x + 2 2. h(x) = logo.25 X 3. 2 + y = log3 X

A: " Since you have asked question with multiple sub - parts, we will solve the first three sub - parts…

Q: log x+ log(x²/y) + log(x³/y²)...... to n terms

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Q: 5. y = log(7x + 3). 4²x¹+8

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Q: 10 y =x X log. Cax+1) logon Do

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

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Q: log(5x) + log(x – 1) = 2

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Q: f (x) = ex ln(5x) - ex^3 +2 + log(e2x^2), find f '(3)

A: The given expression is f(x)=exln(5x)-ex3+2+log(e2x2).

Q: 7 + log(8x) = 28 − 2 log(x)

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Q: 69. y = log;(x – 1) – 2

A: Question number 69,Given,          The function is y=log3x-1-2.

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

A: Given

Q: Differentiate : a. y=log2√x b. y= 2x^(3x) c. y = (x+1)^x

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Q: 2 log3 (x) + + log3 (y) is equivalent to: 2 log3 (ry) O log3 (2ry) O log, (2*y) O log, (zy)

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Q: a) f (x) = 7x log 3x b) f (x) = 3*

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Q: 2 log (5x)-3=1

A: We have to solve the logarithmic equation, 2 log5x-3=1 We know properties of logarithmic, m…