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Math Help - 5 ^ x-2+log 4(base 5)=20 find x?

  1. #1
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    5 ^ x-2+log 4(base 5)=20 find x?

    also for 2logx^2 (base 3) + 2log(3 sqrt x) (base 3) =7 i got x=1.65 is this correct

    the first question is 5 ^ (x-2+log 4(base 5))=20 find x? sorry
    thanks
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  2. #2
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    Quote Originally Posted by b0mb3rz View Post
    also for 2logx^2 (base 3) + 2log(3 sqrt x) (base 3) =7 i got x=1.65 is this correct
    ???

    2\log_3x^2+2\log_33\sqrt x=7

    \Rightarrow\log_3x^4+\log_39x=7

    \Rightarrow\log_3\left[x^4(9x)\right]=7

    \Rightarrow\log_39x^5=7

    \Rightarrow9x^5=3^7

    \Rightarrow x^5=3^5

    \Rightarrow x=3.

    the first question is 5 ^ (x-2+log 4(base 5))=20 find x? sorry
    thanks
    5^{x-2+\log_54}=20

    \Rightarrow5^x5^{-2}5^{\log_54}=20

    Can you finish it?
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  3. #3
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    does this simplify to

    4( 5^x 5^-2) = 20
    therefore x=3???
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  4. #4
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    Quote Originally Posted by b0mb3rz View Post

    does this simplify to

    4( 5^x 5^-2) = 20
    therefore x=3???
    Correct.

    4\cdot5^x5^{-2}=20

    \Rightarrow5^x5^{-2}=5

    \Rightarrow5^x=125

    \Rightarrow x=3
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