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

Q: [2 2x log 2x dx

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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: 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: Condense each logarithmic expression.

A: We have to condense the following logarithmic expressions -  (a) 12log x + 3 log(x+1)⇒ log(x)12 +…

Q: Find the value of x satisfying log,, (2×+x– 41)=x (1 – log1,5).

A: It is given that, log10(2x+x-41)=x(1-log105)   Here logarithmic properties are going to be useful to…

Q: Evaluate the integrals

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

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Q: 9) logx-1(4x – 4) = 2

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Q: 25łn²(x) log (x) dx

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Q: 3 1. y = logVV12x %3D

A: 1. Given function is y=log12x3. Solution: We know that, logab=b loga Given function can be…

Q: f (x) = sec(3x – 1) * log3(2 +x) -

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Q: 9. 8) logx -2 4. 3. I|

A: we have to find logx34=-23

Q: ii) 2 log, (x)– log2 (3x – 4) = log, (x – 1) – 1

A: We make the coefficient 2, exponent inside the log.  And for 1 we replace it by log22 because…

Q: 1. Show that (a) Log(-ei) = 1 - ži;

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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: Suppose that a population grows according to a logistic model with carrying capacity 6500 and k =…

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Q: 8. Solve the equation log (3x+1)-log 2 = log11 for the value of x.

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Q: 1+ax dx Evaluate log 1-ax x 1-x

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Q: x² 6 + ,X log (x² + 7)(x³ – 5)² -

A: Laws of Logarithm:

Q: (x-3 x0t5)Y Sin(lgx) Sin(logx) %3D

A: Cauchy Euler second order differential equation Let us consider differential equation of the form:…

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

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

Q: (b) 5" (2 – cot 5")(1 – csc 5“) dx SC 11 – 2 log x (c) / dx JIV6 log r – logʻ 1 x/6 log x -

A: You have asked Only part b and c

Q: Q3\ Solve for x: a. log(20x + 1) – log(x – 2) = 2 b. In(x - 2) + 2 in Vx+ 3 In6 %3D

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Q: 2. Evaluate sin2x logtanx dx

A: Use the property of the definite integral and simply solve it.

Q: The half-life of plutonium-241 is 13 years.  What is the decay constant?  Use the approximation…

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

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Q: 11 2 log a dx aV6 log r- loga

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Q: #12. SOLVE THE EQUATION а. log (x²) = (log x)² 1 or 100 b. log Vr – 9 = 2 V 10,009 С. log (x³) =…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: In (x + 4) + x = 5 log log (x + 1) +3

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Q: Expand ln 3√y3z2/x4 as a sum, difference and/ or the consent multiple of logarithms.

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Q: Differentiate log(x² + 1)² 4 log10 e а. x2+1 4x log10 e b. x2+1 a.

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

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: d -log(z) = dz (Z

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Q: Following the birth of a​ child, a parent wants to make an initial investment P0 that will grow to…

A: detailed solution is given below

Q: dz Solve dx log (log 2)². z =

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Q: log/ yx-y+3 1-4xt y 4X - log 3 4x ニ

A: Graph

Q: Example 52. x log x dx.

A: Evaluate:∫x log x dx

Q: 2 In 2 log2 x dx 7- S

A: Here I am attaching image so that you understand each and every step.

Q: 0/= log10 (x) dx

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Q: Solve : log z + log 2 = 1 10 100 2. O = 2 T -1 1. -

A: We have to check

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

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Q: 4. Solve for x: a. 100(1.04)²x = 300 b. 2+ log v1+ x + 3 log VT–x = log v1 – x² c. V35x-I = 9 d.…

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Q: 10 logat 1) y = -

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

Q: 1. y = -3+log, r 2. y = log, (r – 2) 3. y = - log, (æ + 3) 4. y = 2 + log,

A: we have to match

Q: Express th equation in exponential form.

A: (a) Given expression is log35=x. Express the above equation in exponential. logab=c, then…

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

A: We have to prove the result.

Q: 1の4--9 aub FVAM ATを l0gb logA 164 こ てレフ)

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Q: 13. Solve for x. log₂ (2x + 3) = 2 log₂ (x)

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Q: 3. 3y +1 = y – 1 4. logx = log 40 – log (x – 3)

A: The objective is to solve the above equations.