Using the change formula, determine which of the following logarithms has the same value as log64(1/16) .(1 point) Responses log27(19) logarithm subscript 27 baseline left parenthesis Start Fraction 1 over 9 End Fraction right parenthesis log36(1216) logarithm subscript 36 baseline left parenthesis Start Fraction 1 over 216 End Fraction right parenthesis log16(164) logarithm subscript 16 baseline left parenthesis Start Fraction 1 over 64 End Fraction right parenthesis log12(18)
To find the logarithm with the same value as log64(1/16), we can use the change of base formula:
log64(1/16) = log(1/16) / log(64)
Calculating the log(1/16) and log(64), we get:
log(1/16) = log(1) - log(16) = 0 - log(2^4) = -4 log(2) = -4 * 0.3010 = -1.204
log(64) = log(2^6) = 6 log(2) = 6 * 0.3010 = 1.806
Now substitute these values back into the initial equation:
log64(1/16) = -1.204 / 1.806
Simplifying this expression, we get:
log64(1/16) ≈ -0.667
Therefore, the logarithm that has the same value as log64(1/16) is log16(164).