Answer:
[tex] \log_2 16 = 4 ~~\Longleftrightarrow ~~ 2^4 = 16 [/tex]
Step-by-step explanation:
[tex] \log_b x = y ~~\Longleftrightarrow ~~ b^y = x [/tex]
[tex] \log_2 16 = 4 ~~\Longleftrightarrow ~~ 2^4 = 16 [/tex]
Keep in mind that a log is an exponent.
When you are asked for the log base 2 of 16, you are being asked for the exponent you need to raise 2 to, to get 16. The base in the log is the same base as in the exponential form.
In other words, the question "what is log base 2 of 16?" is the same as the question "what exponent do you raise the base 2 to to get 16?"
