Q1. Solve In(x) = 9. Q2. Simplify 4 loge (2e) — 3 loge (3e), expressing your answer in the form a + loge (b) - loge (c), where a, b, c are integers. Q3. Solve log₂ (7) = log₂ (x) + 3, for x > 0. Q4. Solve loga (2p + 1) + logµ(3p — 10) = log (11p), for p > 4. Q5. Solve log₁1 (4x + 3) – log₁₁(2x − 3) = 1, for x > 2. Q6. Solve ex = 7. Q7. Solve 53x+1 = 40. Q8. The mass, G, of a radioactive sample in grams after time, t, measured in years is given by the following formula: G = 100e-3t a) What is the initial mass of the sample? b) Radioactive materials have a "half-life" - the length of time required for half of the sample to decay. Find the half-life of this radioactive sample.

Q: (b) If 2log 5+log 4 = 2, find a.

A: The given equation is: 2loga5+loga4=2   As we know the logarithmic properties; 1). logaxb=a·logab…

Q: 5. Solve log 3x² - 5x=1 Solution [3T]

A: Solving an equation is to find the point where the function intersects the x-axis. Sometimes all…

Q: Which value(s) satisfy the following equation? log₂ (x²) + 2log 8 X 392 log₂ (x³) +20 log (32) > 0

A: We need to solve the equation. x=883,262,922.38

Q: 1. Explain the process to solve the equation log, 5 + log,(x - 3) = 4.

A: To solve the equation,  (logb 5) + (logb (x - 3)) = 4 Identity :  (loga M)+ (loga N) = loga MN

Q: Solve for x in log,(x+1) + log4(x – 1) = log4 15 . A. x= 5 В. х3 4 C. x= 14 D. x= 3 or x = 1

A:

Q: Q4. Write in simpler (1) log() 3/4 form 3 (2) log (1)³

A: Here we have to simply it.

Q: Simplify and solve log; v9.

A: We have to simplify and solve the expression log59

Q: 5. Solve for x without using a calculator: log. (x) + log,(x – 16) = 2

A: The answer is found in step-2

Q: x = log (5) - log(10)

A: To solve the single unknown.

Q: Hw/ Selve: O log(x)+log (a-) = log (8K-1a)-legL2) Anyx,3 An s/K=3

A: Here we have to solve ,  a) log(x)+log(x-1)=log(8x-12)-log(2)b) 2ln(x)=ln(3)+ln(6-x)

Q: Solve for x: (log4(log3(log, x))) = 0

A:

Q: 4. Solve for x log (35-x³) log (5-x) = 3

A: Given log35-x3log5-x = 3

Q: What is the domain of the function g(x) = 3 log₂ (x-1) + 4?

A: I am going to solve the problem by using some simple algebra to get the required result of the given…

Q: log₂ (x + 5) - log₂ (x - 2) = 3

A:

Q: 5. [ACS] Determine the following values: (a) Log(i) (b) Log(1 + i) (c) Log(√3+i).

A:

Q: 4. Solve: log2 (5m - 2) log₂ (m + 2) = 2

A:

Q: 5. Solve the equation log(x +2)=1- log(x – 1). Identify any extraneous roots.

A: Solution

Q: 9. Solve. log,(x- 3)+ log,(x+ 4) = 3

A: The objective is to solve.

Q: State any extraneous roots. Show all your work. logx -log(x + 2) = log(x − 3)

A:

Q: 4. Solve the equation log, (x - 3) + log, (3x – 2) = log, 18. Round answers to two decimal places. V

A:

Q: ) log(x − 1) − 1 = − log(x + 2)

A: Given,             logx-1-1=-logx+2

Q: L (a) Logx = 100 x²+2x-24=0

A: ( a ) log x2 = 100formula used log ( x )y = ylog( x ) log ( x ) = k ( x ) = ( 10 )k

Q: Solve for x:logs (2x + 2) - log5 (x + 1) = log5 (x-1)

A:

Q: 4. State the restrictions and solve: log2 (x2 + 6) = 1+ log2(2x + 1)

A: Given: log2x2+6=1+log22x+1 To solve the given expression simplify to obtain the value of x.

Q: 4. log5 (x - 10) = 2 - log, .

A: We need to solve the given equation for x: log5x-10=2-log5x This can be evaluated as follows:

Q: 16. Solve. a) log (²x) = Text 2 b) log4(x²7x − 18) - log4(x + 2) = 3

A: a) log3⁡(2xx−7)=2