In(x + 25) – In(x – 1) = 3 e2x – 2e* = 15 e2x – ex – 12 = 0 e* – 12 = 0 |

Q: Number 3.  Solve the following equations for x: (a). 82x = 2x + 5 (b). log4 (7x + 1) = 3

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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: Express the following logarithms in terms of ln 2 and ln 3.a. ln 0.75                 b. ln (4/9)

A: (a) ln 0.75 = ln (3/4) = ln 3 - ln 4 = ln 3 - ln 22 = ln 3 - 2 ln 2 Hence the answer.

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

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

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Q: Solve the following equations a) 3(2***)-1= 8 b) logg(x +3) =1- log,(x+ 4) c) 7*-4 +3 = 9 d) In(x–…

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Q: Solve the following equations for x (a) 31-x - 92x (b) log2(z – 2) + logą z = 3

A: On solving the first

Q: 1. Solve the following equations a. 4x + 3 = 210 b. 7x - 1 = 3 c. log(8x -15) - log3 = log(2x +…

A: Part a,Given,          4x+3=210

Q: Express the solution in exact form. log 4(x - 5) + log 4 (X – 5) = 1 O A. {7} О в. {-26, 26) O c.…

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Q: Find the solution for x: log (Vz+1+1) log V- 40 -3

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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: Q2: Solve the Logarithms Equation. n = 3 logtan nx (2 + 4 cos?nx) = 2

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Q: 1) Solve for x and y in the following simultaneous equations *a) log, x = 2; 5y= x +12 log, y *b)…

A: We have to solve for x and y in the following simultaneous equations.

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 equation for x: log42 x + log42(x − 1) = 1. If a solution doesnt work, enter DNE. Make…

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Q: Given the following equations, find x log(x – 3) = 3 b. In(x - 2) = 5 – In(2x + 1) c. log2 ) = 3 +…

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Q: If logy =c- log,x, where y> 0 andx > 0, then y is equal to A. c-X В. 3 D. C.

A: To solve the given logarithm

Q: Solve the following equation: 2 log x = log(6x + 27) O x= 3 O None of these O x= 9 X = -9

A: We will solve the equation and will find the value of x as following .

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

A: See the details solution in below

Q: D) log3 (x² – 5) = 2

A: To solve the equation for all real values of x log3(x2-5)=2

Q: (d) Solve the following equations for x. (Correct to 4 decimal places) (i) 2ex-1 = 4 (ii) log5 x –…

A: Brief answer is given 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: Find the solution for x: log (vz+1+1) log Vz- 40

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Q: d. y= 2xe2x e. y= log2(2x2 + 1)

A: The objective is to find  dy/dx.

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: If y = loge (2x + 1)'/2 ? and x = 1 y'will be equal to Select one: O a. 1.3

A: The given function is y=loge 2x+112. Obtain the derivative as follows. dydx=ddxloge 2x+112=ddx12loge…

Q: D. Solve for the following logarithmic equations 1. Inx = -3 2. 2logx = log 2 + log(3r 4) 3. logs(x…

A: As per our guidelines we are supposed to answer only first three sub parts of the question. Kindly…

Q: Given z=(3+2i), solve e^logz

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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: (c) Solve for x given 1≤log, (x-6) ≤3.

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Q: d) log2 (2x2 – 5) = 3.65

A: To Solve the equation for all real values of x Given the equation  log22x2-5 = 3.65

Q: Solve the following equation for X log(x+2) + log(x-1)= 1

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Q: y = log, (2a – 1) · (x³ – 4x)

A: Given: y=log42x-1·x3-4x Formula used: Product rule: f·g'=f'·g+f·g' Constant multiple rules of…

Q: Solve the following logarithm problem for the positive solution for x. 1 log, = -2 %3D 49

A: x=?

Q: Express the equation in logarithmic form. (a) ex+2 = 0.3 (b) e0.2x = t

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Q: Solve for x for each of the following logarithms. Give EXACT answers. 42x-1 = 3**2 log Vx -48x =1 a.…

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Q: 2. 2 log x – 1 = log(x-1)

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Q: 4. Solve the following logarithmic equations: a) logx+log(x+15) =2 b) log,(x+1)= 1 +log, x d)…

A: We have to find value of x for given problem

Q: Solve the following logarithmic equations. a. 〖log〗_3 (x-4)+〖log〗_3 7=2 b. log(3x-13)=2+log⁡x

A: The explanation of answer as follows

Q: Solve the following equation for x. log2(12x + 10) = 3 + log2(x + 2)

A: To solve the given equation for x.

Q: Solve the following equation for x. log;(3x+ 2)+ log;(2x + 1) = 2. 1) -2.6263 2) -0.4975 3) 1.4596

A: The given equation is log53x+2+log52x+1=2. The following rules of logarithms are used in solving the…

Q: In the equationf (x) = e* In(11x) – e**+* + log(e6x*), find f '(3). %| -

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Q: r x2 - 5x +3 х3- 4х2 + 3х -dx Express your answer as a single logarithm

A: Given: ∫x2-5x+3x3-4x2+3xdx

Q: y = log,(x + 3)

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Q: Solve the following logarithmic equation: K•3 B-5 log2(x – K – B – 3) = log2 (x + K + B – 12) %3D

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

A: The given logarithms equation is  logtan nx(2 + 4cos2nx) = 2

Q: Solve the following equations: (a) log x 2 = log(x + 4) (b) 4 3x−1 = 72x+3

A: (a) We have to solve logx2=logx+4 Use logarithmic property logm=logn⇒m=n Hence,…

Q: Please solve the following equations: (a) ln(25(1.05)x)=6 (b) log(1 − x) − log(1 + x)=2

A: Part (a)