Question

what is the solution to the equation (3^{2x - 1} = 243)?

a) (x = -2)
b) (x = 3)
c) (x = 4)
d) (x = 2)

question 10 (5 points)
write (5^4 = 625) in logarithm form.

a) (log_4 5 = 625)
b) (log_5 625 = 4)
c) (log_5 4 = 625)
d) (log_4 625 = 5)

question 11 (5 points)
given that (f(x) = 3^x), identify the function (g(x)) shown in the figure.

Explanation:

Solve the exponential equation

$$
LATEXBLOCK0
$$

Convert exponential equation to logarithmic form

$$
LATEXBLOCK1
$$

Identify the transformed function g(x)

$$
LATEXBLOCK2
$$

Answer:

Question 1

• (A) \(x = -2\)
• (B) \(x = 3\) (Correct answer)
• (C) \(x = 4\)
• (D) \(x = 2\)

Question 10

• (A) \(\log_4 5 = 625\)
• (B) \(\log_5 625 = 4\) (Correct answer)
• (C) \(\log_5 4 = 625\)
• (D) \(\log_4 625 = 5\)

Question 11

• (A) \(g(x) = 3^{-x} + 2\) (Correct answer)