algebra/logs

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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.

  • algebra/logs -

    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>

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