Question

What value is equivalent to log_4 (2.1) to the nearest thousandth? Use the change of base formula to determine your answer. (1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for log_4 (2.1), we can use the change of base formula:

log_a (b) = log_c (b) / log_c (a)

In this case, a = 4 and b = 2.1, so we can rewrite log_4 (2.1) as:

log_4 (2.1) = log (2.1) / log (4)

Using a calculator to find log (2.1) ≈ 0.322, and log (4) = 2, we can plug these values back into the equation:

log_4 (2.1) = 0.322 / 2 ≈ 0.161

Therefore, log_4 (2.1) is approximately equal to 0.161 to the nearest thousandth.