algebra/logs
posted by Nancy on .
I don't understand this problem:
(1/2)n = 0.015625
n log 0.5 = log 0.015625
n = log 0.5 / log 0.015625
n = 6
When I plug log .5 into the calculator it gives .3010 and when I plug .15625 to the calculator it is 1.806 and that would be .3010/1.806 =.1666. How is the answer 6? Really, can you provide a detailed explanation? I am really confused.

It's because you should have divide by log .5:
n = log 0.015625 / log .5
Note that .16667 = 1/6, the reciprocal of the answer.
<ouch> slap forehead! </ouch>