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)

1)0.287
2)1.868
3) 0.535
4) 0.081

1 answer

3) 0.535

Using the change of base formula, log_a (b) can be rewritten as log_c (b) / log_c (a), where c can be any base.

Therefore, log_4 (2.1) can be rewritten as ln(2.1) / ln(4) (where ln represents the natural logarithm).

Calculating ln(2.1) ≈ 0.741, and ln(4) ≈ 1.386.

Therefore, log_4 (2.1) ≈ ln(2.1) / ln(4) ≈ 0.741 / 1.386 ≈ 0.534969.

Rounded to the nearest thousandth, log_4 (2.1) ≈ 0.535.

So, the answer is 3) 0.535.