5. Solve the following logarithmic and exponential equations: points) (a) log(x +2) = log(3r – 6)

Q: 13. Combine the following into a logarithm: single 2 log – 3 log y + log(x*y²)

A:

Q: 18. Solve the following logarithmic equation: In(x + 31) – In(4 – 3x) = 5 ln 2. O x = 2 O x = 1 O x…

A:

Q: 14. Solve the equation: log3 (x + 1) + log;(2r – 3) = log, 9

A:

Q: 4) Consider the following logarithmic equation: What is the solution to the equation? log4(x + 2) +…

A:

Q: 2. Solve the logarithmic equation (g) In r = 1 (h) log3 (20x + 31) = 4 (i) log;(449 – 7x) = 3 |

A: Solve the following

Q: 2-Solve the following logarithmic equations. a) Log, 2 – log 4 b) 2 + 5(3*) =3(3*) x +7/6=0 -

A: We have to solve the given logarithmic equations to find the value of the variable x. For this, we…

Q: Given that ln(5) = x and ln(7) = y, express the given logarithmic value in terms of x and y.…

A: Given that ln(5) = x and ln(7) = y. Use the property of the ln function

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

A:

Q: What is the family of the equation y = log,(x) O quadratic linear O logarithmic Fill in the table of…

A:

Q: 1. Solve the equation: a) e -3 b) 25* -s 125-S c) log vx – 6 = 1

A:

Q: 2. a. Solve the following exponential equation: 3* x 53x+m = 160 b. Simplify the following…

A: In part a. we need to solve for x and in part b. we need to simplify the given logarithmic…

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: how do i condense this expression to a single logarithm? step by step please

A: The given logarithmic expression is

Q: (1) Solve the following: 1 (i) 2*/2-16 32 (ii) log, (x-2)+ log, (x) = 1 %D

A:

Q: 12.) Use the laws of logarithms to combine: 2 log x + 1 log(x² + 1)

A: We have to use the laws of logarithms for the given equation.…

Q: 2. Given that x> 0, the value of x for which log, x + log,(6x + 1'0) = 1 is D

A:

Q: (1) solve the following  i) 2x/2-16  = 1/32  ii)  log8 (x-2) log8 (x )= 1

A: We have to solve and finding the value of x  Here using logarithmic properties

Q: 3(1 + 108x) = 8 %3D (a) Find the exact solution of the exponential equation in terms of logarithms.…

A:

Q: A function defined by y = ab can be written in terms of an exponential function base e as

A: The function is y=abx

Q: Find the solution of the exponential equation 15e^x−13=6 in terms of logarithms, or correct to four…

A: We have to solve

Q: 4. The domain of the logarithmic function f(x) = log, x is

A: fx=logax

Q: solve for x in the following equation 2e^3x-1=10

A: To solve the equation

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

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Solve graphically with your calculator. Round answers to 2 decimal places. а.) 4* = VE b.) log r =…

A:

Q: D) log3 (x² – 5) = 2

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

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

A:

Q: 2. Solve for x. log,24 – log,2 = logax

A:

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: 2-Solve the following logarithmic equations a) Log, 2 – log 4 x +7/6=0 b) 2 + 5(3*) =3(32*)

A: logx2-log4x+76=0log2logx-log4x+76=01logxlog2-log4x+76=012logx2log2-log4x+76=012logxlog22-log4x+76=01…

Q: 1) lag is equal to logizs b)3, c) 3x .d) none of them

A: Solution: log5xlog125x=log5xlog53x we know, logbna=1nlogba hence  log53x=13log5x hence…

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: 11 2 log a dx aV6 log r- loga

A:

Q: (a) Use the definitions of hyperbolic functions in terms of exponentials to prove that 8 cosh'x cosh…

A: a) LHS =  8cosh4x  =  8(cosh2x)2  =  8 * ((1/2)( cosh(2x) + 1))2  =  2 (cosh2(2x) + 2cosh(2x) + 1)…

Q: 4. Solve the following logarithmic equations. a. 2logx = log2 + log(3x – 4) d. logx + log(x – 1) =…

A: The logarithmic properties; 1). logbmp=plogbm 2). logbm·n=logbm+logbn 3). logbmn=logbm-logbn 4). If…

Q: 9. Solve the logarithmic equation 3+log(2x+5)=2.

A:

Q: B. Convert to an exponential equation. 1. log, T =x 2. t= log, 7 3. In 0.38 =- 0.9676 5. log 0.01 =-…

A:

Q: 3 Solve the logarithmic equation log(x – 1) + log(x – 4) = 1. A {1} (1, -6) B (6} D {-1, 6} E {1, 6}

A:

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: 10. Solve the following logarithmic equation. log (x+ 25) log(x + 10) + log 4 %3D

A: To solve the logarithm  Use formula log a + log b  = log (ab)

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

A:

Q: 7. Solve each equation for y. [Leave final answers in a simplified exact form or an approximate…

A: Given, (a)  ln4y +5  = lny-1  (b) 5-3log4x-3 = -4 We have to solve the equations

Q: 16 Rewrite the exponential equation into its corresponding logarithmic equation. 12 = 144 F log,,…

A: Answer is mentioned below

Q: 1. Solve the equations 2 - x a) 2 – x = |2x + 1| b) 2 = c) log! -2 %3D |x+1|

A: Modulus function is a function which always gives a positive value whatever the input given to the…

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: 3. Solve the logarithmic equation log,x + log2(x-6) = 4

A: Given:   The logarithm equation is       log2(x) + log2(x-6) = 4 The product rule states that sum of…

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

A:

Q: 4. Find the value of x in each of the following logarithmic equations. a) log5 x = 3 b) log, 169 = 2

A: Formula used

Q: 12.) Use the laws of logarithms to combine: 1 2 log x log(x² + 1) - 2

A:

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

A: Given logarithm ln49 The objective is to expression the logarithm in term of  ln (2) and ln(3)

Q: 7. Solve the equation log(x + 2) + log(x - 1) = 2

A: