2. Simplify the following expression •(log,(r – 2) – log,r)

Q: By using u=ln(3x) and dv=6x dx, find ∫ 6x ln(3x) dx. Be sure to include the argument of the…

A: Consider the integral

Q: Express the following logarithms in terms of ln 5 and ln 7. ln 7√7

A: We first write the inner expression using an exponent.

Q: Q2: Solve the Logarithms Equation. logtan nz (2 + 4 cos ?nx) = 2

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Q: 1. Complete the formulas: log, (MN) = r log, x = log, x– log, y = Definition of log: y=c* > Change…

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Q: 4. Use the special properties of logarithms to solve the following equations. a. M = log„1121 b.…

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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: 6. A. Apply the properties of logarithms to expand the following expressions and simplify as much as…

A: Apply logab= loga + logb           loga/b=loga-logb

Q: (1) Expand the following into as many logarithms as possible, with what's inside each simple as…

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Q: Solve the following: 1 (ii) log, (x+3) =1-log,(x-1) r-6 (i) 2" 8.

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Q: Evaluate the following: log, a Find y in terms of x for In(y+1)=2– 3 In.x

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Q: Solve the following logarithmic equation: z=7, k=3 log;(Z + 8)x7 – log3(2K +9)x³ = log;(Z + 5)x² +…

A: Given,         log3Z+8x7-log32K+9x3=log3Z+5x2+4Z+K-6         When Z=7 , K=3

Q: 2. The expression log(3 + x) is undefined for what values of x?

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Q: Given that p = loga 4 and q = loga 5. Express loga 100 + loga 0.4 in terms of p and q.

A: The given value of p and q are p=loga4  and  q=loga5.

Q: 8. Let f(x) = log,(3x² – 2). For what value of b is f'(1) = 3?

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Q: 1) Condense the following logarithr 4log3x + log,v 2) Expand the following logarithm log.()

A: We have to expand logarithm

Q: 3. Given that log,x = 2 and that log, y = 3, use the logarithm laws to expand the following and…

A: \Logarithm rules:logaxy=logax+logaylogaxy=logax -loga yloga x4 =y loga xlogaa =1

Q: 24. For which b does the definition of log,x just given make sense, and why? Is this the same…

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Q: 12. Solve the following equation * 3 poin log, x + log, (x -9)= 2 O 12 О 3, 12 О з 8. O -8 O -2, 8 O…

A: We use the formula logam + logan = loga(mn) logab = c    →  b = ac

Q: Use the logarithm identities to obtain the missing quantity. 2 log,(p) – 4 log,9) – 3 log,(r) = log,

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Q: Use log, 20.401, log, 3≈ 0.503, and log, 5 0.794 to approximate the value of the given logarithm to…

A: Given : logb2≈.401 , logb3≈.503 and logb5≈.794 To find : logb75≈?

Q: What will the coefficient (x – 1)² in the expansion of loge x about x = 1 ? %3D

A: Introduction :

Q: Evaluate loge 7 by Simpson's (i) rd, and (ii) th rules.

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Q: 5) Show the proof that loga M" = r· loga M

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Q: Write the following expression as a single logarithm with coefficient 1: In (2z") – In(3z°) +…

A: Given- ln2x9-ln3x6+ln8x7 To Write- The above expression as a single logarithm with coefficient 1.…

Q: 2. Express the indicated logarithm in terms of a, b and c with the assumptions that log 2 = a, log 3…

A: To express the indicates logarithms in terms of a,b and c.

Q: 17. Find the value of x without the use of calculator 1 log, 3. 4

A: Given:

Q: 2 Which of the following is equivalent to log,(m) logm(20) ? 80 H log(5) log(m) K log.20

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Q: 8. Write as the sum and/or difference of logarithms. Express powers as factors. Vx +3 (x - 4)5\ In…

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Q: Given that x, y, z >1 and w be a positive number such that log, w = 24, log, w = 40 and logrvz W =…

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Q: -Given that p log, 5, q log, 2 express the following in terms of p and/or q. log, 0.625

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Q: 3 [og,x + logy] – 2[log,a + log, V5]

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Q: (8) Expand the following into as many logarithms as possible, with what's inside each logarithm as…

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Q: 6) Given that x = log, b. write down an %3D expression for b in terms of a and x. log, t that log, t…

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Q: Suppose log, (X) = 1.4, log,(Y) = 2.2, and log, (Z) = 2.4. Evaluate the following two expressions.…

A: To find the required value of logarithmic expressions. We use some basic properties of logarithmic…

Q: Suppose log, (x) = 2 and log, (y) = 5. Find the following: d) log.(V) e) log, (x + 2y) f) log,(y")

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Q: 4. Solve the following logarithmic equation: log; (Z + 8)x7 – log3 (2K + 9)x3 = log3 (Z + 5)x2 + 4(Z…

A: Here, Z=9k=5

Q: 2. Given p = 2' and q = 2', express log, p'q in r and t terms. 64

A: Given

Q: (a) Solve the following: (ii) log,(x+3)=1-log,(x-1)

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Q: 5. Prove if the following function is differentiable y = x loge-*

A: Given that: y=xloge-x

Q: 7. Find y'. y = log, (9– x-x)

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Q: Given that h(x) = log(x + 1) and f(x) = 2+ 10², find and simplify foh(æ)).

A: Composition of two function f(x) and g(x) is the process of making a new function h(x) such that the…

Q: 2) Evaluate the following without using a calculator. Show your work. a) loga 8 = b) log: (

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Q: b) Given that log, (y-1)+log,|| |= z and log, (y+1)+log, x = z-1, Show that y? =1+8² and find the…

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Q: 4 Given that log 20.571, log 4≈ 1.141, and log 6≈ 1.476, find log n 4 log nr (Type an integer or a…

A: This question is from logarithm and its property

Q: Express the following logarithms in terms of ln 5 and ln 7. ln (1 / 125)

A: Express the following logarithms in terms of ln 5 and ln 7. ln (1 / 125)

Q: 2. Prove the following equations: A. HOg, 6 = 1 logab a 1+log, b B. log1 a? = -2

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Q: 3-Given that a=log, 3 and b=log ,6, find log, 24 in terms of and b

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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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