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
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.