Using the change formula, determine which of the following logarithms has the sam value as log_64 (1/16). (1 point)

Answer 1

log_4 1/8

To determine if this logarithm has the same value as log_64 (1/16), we can use the change of base formula for logarithms:

log_a b = log_c b / log_c a

First, rewrite log_64 (1/16) using the change of base formula as:

log_64 (1/16) = log (1/16) / log 64

Now, simplify log (1/16) and log 64:

log (1/16) = log 1 - log 16 = 0 - log 2^4 = -4 log 2

log 64 = log 2^6 = 6 log 2

Now, replace log (1/16) and log 64 in the change of base formula:

log_64 (1/16) = (-4 log 2) / (6 log 2)
= -4/6
= -2/3

Therefore, the equivalent logarithm is log_4 1/8.