11. Condense the expression log, (x² – 3x+2) . +2log(x+1).

Q: m=4 , n=5 2 log, 641.B = <+3 = 4 10 1.c=* 2. LetA = 4 4 21 т -7 and D = -1 Find X, if ABT +…

A: Two matrices A=a1a2a3a4 and B=b1b2b3b4 can be multiplied using the rules of matrix multiplication.…

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: 7. The expression 4 log x -- log y + 3 log z can be rewritten equivalently as (x*z' (3) log 2y (1)…

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Q: 2) 22x = 20*-1, Leave your answer in the form logg A, where A and B are whole %3D numbers.

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: Express th equation in exponential form.

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Q: Solve the following: 1 (1) 2*-6 8 (ii) log,(x+3)=1- log,(x-1) =-

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Q: Express the following using a single log: 3Log ab2 -Log a2b - 4 Log a/b - 3Log b2

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Q: Solve the following equation: 2logx - log3 = 2 9√/3.7 O-11√2 10√3 O-10√/3.1

A: We can solve the given function.

Q: 17. Expand the expression Vx+1(x² - 4) |ninon se log2 183 (r°+27)* -3 081 2

A: Given expression

Q: Estimate the error in the value log 2.7 obtained from the following dată.

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Q: 9⋅7x=3.5e^(2x) Find x using natural log

A: Given exponential equation is:Solve for x using natural log.

Q: Suppose that a and y are real numbers such that log2 (x) = – 3 and log2 (y) 6. Calculate the…

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Q: at any point h (1, 1) is logx – x

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

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Q: , Find the solution for x: log (Vz+1+1) log V- 40

A: See the details solution in below

Q: Solve the following equations: 2 x³ = 49 3*.27*=9 √5*=25(x-1) d. b. log₂ (6x-4)=-1 28=2(5*)

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Q: B. Express as a single logarithm and, if possible, simplify. 1. log, x + 4 loga y – 3 loga x 6.…

A: This is a problem related to logarithm properties. Based on the general formula we can answer the…

Q: Determine if the given functions are LI or LD by computing the Wronskian : -2x Yi = e*,y2 = e*,y; =…

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Q: O f (x) = – log(x – 2) - -

A: Given: The functions, f(x) =12x - 2f(x) = log2 ( x +2)f(x) = - log ( x -2)f(x) = ln x + 2 f(x) =…

Q: 3. Express as a single logarithm: 3 log 2 + log x - log (4x) log(8x) A. log(4x) В. log (2) C. log…

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Q: (b) 2log(x – 3) – log(x – 1) = 0

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Q: 2 log , x + 12log, y

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Q: 4. What is b if (log, x)' :? Зх

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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: what is the domain of the function Y= logy (9x t 12) - 5?

A: y=log44x+12-5

Q: 7) Propose an equation similar to log 4 + log x = log 27 whose solution is 9 %3D

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Q: Given 2 log3(x + y) = 2 + log3x + log3 y, show that x² + y² = 7xy.

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Q: 9

A: We need to solve

Q: b- find x for following 1. logx = v2

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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: 8. Let b be a positive real number not equal to 1. Determine the solution of the equation log, (2z –…

A: See the solution step by step.

Q: 4. Find the solution set of log3 (2x +6) + log3 (2x-2) = 2. |

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

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Q: 2. Rewrite as a single log (condense): 7 5, loga (xy®) +12lo9 x12 - 5log. (y) 16,,8 8

A: Answer and explanation is given below

Q: Evaluate gradø if 9= log(x² + y² +z')

A: Consider that the gradient of a scalar function ∅x,y,z is given by, grad ∅ =i^∂∅∂x+j^∂∅∂y+ k^∂∅∂z…

Q: If (5)** = 16 and log x-y8 =- 3, calculate the values of x and y. %3D

A: lna(b)=y then b=ay  (am)n=amn

Q: direct

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Q: 2 log(x+y) = 3log3 +logx + logy

A:

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

A: Given that: y=xloge-x

Q: 2. Rewrite in terms of a single log (condense): (15log. (x) + 10log. (v)]– 7[3lo9. (x) + loga (v)] 5

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Q: 2. Solve for x, to one decimal place. (b) 7* = 35 %3D (a) log, 56 = x

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Q: - 4 ) if f(x)= log3 3-2 (x3 – 4) (x3 – 2)In(3) 6x? %3D (..3 ..3

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Q: Show that 2 + 11n² log,(n³) – 7 = 0(n³)

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Q: Given that log, x + 2 log4 y = 4, show that xy = 16. Hence solve for x and y in the simultaneous…

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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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Q: 3 x4 Vx2+1 Differentiate y = (3x+2)5 (Hint: Take the natural log of both sides first)

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Q: t(z)= 2z log2z  , t '(z)?

A: