Question

what is the approximate value of \\(x\\) in the equation below.

\\\log_{\frac{3}{4}} 25 = 3x - 1\\

-3.396
-0.708
0.304
0.955

Explanation:

Apply the change of base formula

$$ \log_{\frac{3}{4}} 25 = \frac{\ln(25)}{\ln(0.75)} \approx \frac{3.218876}{-0.287682} \approx -11.1888 $$

Set up the linear equation

$$ -11.1888 \approx 3x - 1 $$

Solve for x

$$
LATEXBLOCK0
$$

Answer:

• (A) -3.396 (Correct answer)
• (B) -0.708
• (C) 0.304
• (D) 0.955