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Math Help - Quick Question

  1. #1
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    Quick Question

    Im working on a question and Im almost done but i cannot simplify it. So the question is 8 to the power of what equals 16? OR 8^X = 16

    PLEASE HELP ASAP!
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  2. #2
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    Quote Originally Posted by Nikola View Post
    Im working on a question and Im almost done but i cannot simplify it. So the question is 8 to the power of what equals 16? OR 8^X = 16

    PLEASE HELP ASAP!
    Remember that 8=2^3 \mbox{ and } 16=2^4

    so now we get

    \left( 2^3 \right)^x=2^4  \iff 2^{3x}=2^4

    Since the bases are equal the exponents must be equal. So we need to solve

    3x=4 \iff x=\frac{4}{3}

    This problem could also be done using logs.

    I hope this helps.

    Good luck.
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  3. #3
    Moo
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    Hello !

    Quote Originally Posted by Nikola View Post
    Im working on a question and Im almost done but i cannot simplify it. So the question is 8 to the power of what equals 16? OR 8^X = 16

    PLEASE HELP ASAP!
    You can use the logarithms, or better :

    8^x=16

    8=2^3 and 16=2^4

    ---> (2^3)^x=2^4

    2^{3x}=2^4 (using the (a^b)^c=a^{bc} rule)

    So 3x=...



    Edit : still too slcow !
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  4. #4
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    Quote Originally Posted by Moo View Post
    Hello !


    You can use the logarithms....
    8^x=16\rightarrow\log_8{16}=x

    \log_8{16}=\frac{\log_{10}{16}}{\log_{10}{8}}=\fra  c{\log{16}}{\log{8}}=\frac{4}{3}
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