Question

Use the Change of Base Formula to evaluate log274.(1 point)Responses4.3044.3045.9045.9046.2096.2091.869

Answer 1

To use the change of base formula to evaluate log274, we can rewrite it in terms of a known base. Let's use base 10 for this example.

The change of base formula states that for any positive number a, b, and c:

logc(b) = loga(b) / loga(c)

We want to find log274, so we can use base 10 as our known base:

log10(4) / log10(7)

Since log10(4) is not a known value, we can approximate it using a calculator:

log10(4) ≈ 0.602

Similarly, log10(7) is not a known value, so let's approximate it:

log10(7) ≈ 0.845

Now we can substitute these approximations into the change of base formula:

log274 ≈ 0.602 / 0.845 = 0.713

Therefore, the approximate value of log274 using the change of base formula is 0.713.

So the correct response is 0.713.