What value is equivalent to log4 2.1 to the nearest thousandth? Use the change of base formula to determine your answer.(1 point) Responses 0.535 0.535 0.081 0.081 1.868 1.868 0.287

Answer 1

To determine the equivalent value of log₄ 2.1, we can use the change of base formula.

The change of base formula states that logₐ b = logᵧ b / logᵧ a, where a, b, and ᵧ represent the bases of the logarithms.

In this case, we want to find the value of log₄ 2.1, so a = 4 and b = 2.1.

Using the change of base formula:
log₄ 2.1 = log₂ 2.1 / log₂ 4.

To calculate log₂ 2.1, we can use a calculator:
log₂ 2.1 ≈ 1.086.

To calculate log₂ 4, which is just log₂ 2 raised to the power of 2:
log₂ 4 = log₂ (2²) = 2.

Now we have:
log₄ 2.1 = 1.086 / 2 ≈ 0.543.

Rounded to the nearest thousandth, the equivalent value of log₄ 2.1 is 0.543.