6. Expand the expression 2x+3 log (x+4)°(x- 3)*

Q: Find the first six terms of the expansion of the function e^x log(1+ y)

A: We have to find the first six terms of the expansion of the function              exlog1 + y Here ,…

Q: 4 If log,(x + 1) – log,x = 2, then x equals: F H

A: It is logarithms problem.

Q: .Expand log (1 + sin x) in powers of z as far as the term in r.

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Q: Find the greatest integer less than or equal to log29 S2²10 log₂ (x³ + 1) dx + S₁ 3 (2-1) dx.

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Q: Express x in term of y if: log,xy =2 +2log,x -3log,y

A: Given that:  log4xy=2+2log4x-3log4y We have to express x in the form of y.

Q: Solve each equation.

A: According to logarithimic rule , . If , then .

Q: Given that log4(y-1)+log4(x/2)=z and log2(y+1)+log2x=z-1, Show that y2=1+8z and find the possible…

A: Concept: Logarithm base change rule: logb(x) = logc(x)  logc(b) Logarithm quotient rule: logbxy=…

Q: 4. Find x if the base 3 log of (2x+3) is equal to 4. 30.5 81 O39

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Q: If k is a positive constant, show that x^2 e^-kx approaches 0 as x --> ∞.

A: Given  The x2e-kx approaches 0 as x→∞.Where k is a positive constant .

Q: asb b? =In 2. %3D (3

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Q: 4 Evaluate (logyx)'., having given, 1 1 y = log1,x + ; log,0x + log10x + . 00 1+3+5+ ..+ (2y - 1) 20…

A: We have to solve given problem:

Q: 2. Find y' if y = 7* (log4 x)⁹.

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Q: 19. If logx y + log, x = 2.9 and xy = 128, find x + y. 24 O 20V2 O 36 O 34V 2 O 66

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Q: - Find the solution set of * 2log2 (x + 8) – log2 (r + 6) = 3

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Q: 3. If 19.4 = log (ab) and 7 = log₂ (a), where > 1, then log, (b) equals H 12.4 26 2.8 135.8 ◄ Prev…

A: We want to find the value of logxb.

Q: If log3(3x +5) – log3(9x) = 2 then enter your answer for x as a fraction in its lowest form

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Q: at any point h (1, 1) is logx – x

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Q: 22. Suppose f(x) = log x + log(x – 3). Find the x-value for which f(x) = 1.

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Q: Solve the following d. In 3- Inx - In (x + 5) = 0 e. Log4 (x+ 2)- log4 (x - 1) = 1 f. Log2 (x-1) –…

A: The detailed solution is as follows below:

Q: Use the properties of logs to expand: x+5 b) log+ 3x-2 d) log, x(x + 4)

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Q: Simply the following 1 1.5 Inx – In(x² – 1) + 2ln(x + 3) 2. 5log2 + log3 – log8 -

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 11. Write as a single logarithm: 1 log2 X +3 log2 Y - 3 ·log2 Z

A: To write: The expression 13log2X+3log2Y-52log2Z in single logarithm. Formula used: Logarithmic rule:…

Q: 19. If log,2 = x and log34 =y, then log372, in terms of x and y, is equal to O 2x +2y O 9x +9y O 9xy…

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Q: - y =log x² dy_ 8log, x A. dx dy 4log, x В. dx dy _ 4xlog, x xIn 2 dy 8x log, x D. dx xln2 xIn2 dx…

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Q: . Find the exponential functions of the form f(x) = ab* that pass through 1) (-2, 32) and (1, –)

A: An exponential function is in the general form f(x) = abx We know the points (-2,32) and (1,1/2) ,…

Q: 26. Describe the behavior of each of the following: (a) 5 (b) log x as x>0 as x (c) ln x as x ->co…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 2) y= log, (-4x +6)+ 4 2 +6 1) у3D 4) y= In (4x – 10) – 6 e+10 3) y =

A: SOLUTION- Since you have posted a question with multiple subpart , we will solve first three for you…

Q: Find the integral: log2 X dx In(2)/ 082(x) + C 2

A: Put logx = u then solve it.

Q: Find the exponential function f(x)=a^x that passes through the point (3,343) and has a y-intercept…

A: We have to find the exponential function f(x)=a^x that passes through the point (3,343) and has a…

Q: - f(x) = - f(x) = x-2 g(x) = 5 In x - 2* g(x) = 4x' log, x %3D f(x) = 10* · e*

A: Solution of question is written in below steps.

Q: ,162,20 If log A log(x) + Blog(y) + C log(z) 27 A = В - C =

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Q: 2. i) Now, on your calculators, compute the following: e-24 = log2 3 =

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Q: Suppose that log3(x) = 5.3 and log3(y) = 2.1. Evaluate the following exactly, and show your work a.…

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

Q: 5. Find y' and y". In x (1) f(x)= (2) f(x)= log,o * 6. Find y' if y=In(x²+y?)

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Compute 3 In(e) +2 log(10) 7 11 1 9. 3. B8

A: Solve by properties of logarithm.

Q: thats a natural log of 9 to 0 and integral from 9 to e^x

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Q: If log a= x and log b= y then log (ab^2) equals 1/2(x+y) x+1/2x+22x+2y

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Q: State the restriction(s) on the variable x in log(2x-5) – log (4 - x)

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Q: 7. Find y'. y = log, (9– x-x)

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Q: Solve the following logarithmic inequalities. 1. log5x 2 3. log273 > x 4. log2(5x + 7) > 5 5.…

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Q: 4- If X is an exponential with parameter 1, then 2X is chi-square with 2 degrees of freedom. O True…

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Q: 1. Express the following as a single log 3log xy-log x +log y a) 6log x b) 3log x c) 6log y d) 3log…

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Q: 1. Find for the following functions : dx 2x (ans.: 3x' log,( 3 – 2x)-’ (3–2x )In 2 45) y=x' log,(3–…

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