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Math Help - Which logarithm property is this?

  1. #1
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    Which logarithm property is this?

    In this equation:


    Which logarithm property is used to change log base 4 to log base 2? Is it just an application of the change of base theorem? Everything else makes sense to me but that.

    EDIT: I feel dumb now. I just realized that it's the change of base theorem being used to change the base to log base 2, thus giving a simplified answer.
    Last edited by zsf1990; March 2nd 2013 at 07:21 PM.
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  2. #2
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    Re: Which logarithm property is this?

    Hello, zsf1990!

    Here is another approach.


    \text{23. Evaluate: }\,\log_48

    \text{Let }\,\log_48 \,=\,x

    \text{Then: }\,4^x \:=\:8


    \text{Get the same base on both sides:}

    . . (2^2)^x \:=\:2^3 \quad\Rightarrow\quad 2^{2x} \:=\:2^3


    \text{Equate exponents:}
    . . 2x \:=\:3 \quad\Rightarrow\quad x \:=\:\frac{3}{2}
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