(1) log r'y (3) log VV

Q: Show that the following functions are harmonic in x and y: log√x² + y²

A: Solution

Q: Express the following logarithms in terms of ln 2 and ln 3.c. ln (1/2)           d. ln( 9)^1/3

A: Given: c  ln12  d ln913 Formula Used: 1 lnmn=lnm-lnn2 lnxn=nlnx

Q: Given that log x -3 and log y = 5, find log Vy.

A: The given expression is logx2y35 and logx=3   and   logy=5

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

A: Solve the following integral

Q: s) Use the properties of logarithms to find dx y = In 4] sin' (3x) 5* √√x² +1

A: We can solve the derivative of 'y' as below.

Q: Differentiate the following using logarithmic differentiation. 1. у%3D (x+6)(x+8)8 (r+3)3(r+5)s

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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: (x² + 1)? dy if y Find dx (x² – 1)³ a) without the aid of logarithmic properties b) using…

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Q: Which of the following functions grow faster than x2 as x→∞?Which grow at the same rate as x2? Which…

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Q: Express the following logarithms in terms of ln 2 and ln 3

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Q: | 1-x² y = log10 2- 5x

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Q: Find , given y = log(ev+x²). dy dx

A: Given y=logex+x2  We find dydx The differentiation formula of logarithm is ddxlnx=1x and the power…

Q: By using natural logarithm (ln), find dy/dx for this equation, 384=(x+2)3/4(y+3)1/3.

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Q: Solve the following logarithmic equation:  log x + log(x − 1) = log(4x)

A: Simplify logarithmic equation

Q: f(x) = (a

A: Here, let y=f(x)=x3x3ex3 Taking natural log (ln) on both sides: ln y=lnx3x3ex3⇒ln y=lnx3x3+ln ex3⇒ln…

Q: Express the guven auantity In (xt2)" single logarithm. ' + I LIn x-In (x? + 3x +a)°J as a

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Q: 10. y = log2(3x + 1) %3D

A: We have to solve

Q: What happens to the rate of change of the logarithmic function y = loga x as a becomes larger?

A: What happens to the rate of change of the logarithmic function y = loga x as a becomes larger?…

Q: 5. Find the derivative of the following Natural Logarithm functions f(x) = In(3x – 4) a. b. 2

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

A: we have to rearrange the equation to isolate A

Q: 5. Which of the following functions grow faster than In x as x →o? Which grow at the same rate as In…

A: Hey, since there are multiple subparts posted, we will answer the first 3 subparts. If you want any…

Q: Express the following logarithms in terms of ln 5 and ln 7.e. ln 0.056          f. (ln 35 + ln…

A: Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to…

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

A: Given query is to find the derivative of 2x.

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

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Q: Find the value(s) of x for which the equation is true. log(x + 3) = log x + log 3

A: We have to find the value of x for the given equation: logx+3=logx+log3 We know the properties of…

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

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Q: e ecse with the and of logarcdtlmc dffenatiation /-

A: We have to find the differentiation of the given y

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

A: Derivative.

Q: if võ zo, JT = 1 and Jū= 2 estimate Vo by constructing Logrange pelynemial, then with the exact…

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Q: Sind dx/dy if ys log Vitx? 14

A: Given: y=logx1+x2+logx1-x214. So,         dydx=ddxlogx1+x2+logx1-x214…

Q: 6. Which of the following functions grow faster than In x as x→∞? Which grow at the same rate as In…

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Q: If y = loge(sin x)? dx will be equal to dy

A: Given: y=logesinx. To find: dxdy Solution: Chain rule of differentiation states that:…

Q: Find Y for the following function: dx 3- y = log,(x3- x) 4- y = In 5- tan-1 V4x – 5

A: we have to find the derivative of the following

Q: dz Solve dx log (log 2)². z =

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Q: Find the logistic differen tial equation dy =ky 1- dx

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Q: Find d (7ª). Type In(x) for the natural logartihtm function. dx

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

Q: Find e to as many decimal places as you can by solving the equation ln x = 1 using Newton’s method .

A: Find the derivative of function.

Q: Express the following logarithms in terms of ln 2 and ln 3. ln 0.75

A: To express ln0.75 in terms of ln2 and ln3

Q: 2. x log x +y = logx. dx

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

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

Q: Sind dix/dy ifLys loge vitx? 4.

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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)=5ln x       and g(x)=ln x,

Q: ` log x dx

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Q: Find d/dx(4^x). Type ln(x) for the natural logarithm function.

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Q: Express the following logarithms in terms of ln 2 and ln 3. ln 3√9

A: To express:  ln 3√9 in terms of  ln 2 and ln 3.

Q: log 4z a tall var I

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

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