Question

Using the change formula, determine which of the following logarithms has the same value as log64(116)
.(1 point)

log27(19)


log12(18)


log36(1216)


log16(164)

Answer 1

Use the change-of-base formula log_a(b) = ln b / ln a and compare numerically.

log64(116) = ln 116 / ln 64 ≈ 4.75359019 / 4.15888308 ≈ 1.1429188.

Now the choices:
- log27(19) = ln 19 / ln 27 ≈ 2.944439 / 3.295837 ≈ 0.8935
- log12(18) = ln 18 / ln 12 ≈ 2.890372 / 2.484907 ≈ 1.1630
- log36(1216) = ln 1216 / ln 36 ≈ 7.103322 / 3.583519 ≈ 1.9829
- log16(164) = ln 164 / ln 16 ≈ 5.099866 / 2.772589 ≈ 1.8391

None of these equals 1.1429188, so none of the given logarithms has the same value as log64(116).