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Math Help - question regarding logs

  1. #1
    Junior Member
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    question regarding logs

    hello! there is a question 10to the power of 2log 4 and it is asking me to simplify, but im not too sure how to go about. the base for the log is 10 and not 4 if you were wondering.

    Thx in advance.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Solid8Snake View Post
    hello! there is a question 10to the power of 2log 4 and it is asking me to simplify, but im not too sure how to go about. the base for the log is 10 and not 4 if you were wondering.

    Thx in advance.
    HI

    x^{\log_x(y)}=y

    Proof : Let  x^{\log_x(y)}=p and lets see if p=y

    Knowing that a^x=y\Rightarrow \log_a{y}=x

    \log_x{p}=\log_x{y}

    cancelling the logs , we get p=y so the above is correct .

    Now back to your question :

     <br />
10^{2\log_{10}{4}}=10^{2\log_{10}{4^2}}=16<br />
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