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Thread: logarithm/exponential equations

  1. #1
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    logarithm/exponential equations

    i really need to know how to solve these equations. thanks!

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  2. #2
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    Quote Originally Posted by fishlord40 View Post
    i really need to know how to solve these equations. thanks!


    Assuming $\displaystyle \log a=\log_{10}a$ , and assuming you made a typo and meant $\displaystyle \log\log x$ in the first exer., then

    $\displaystyle \log\log x=3\Longrightarrow 10^3=\log x \Longrightarrow 10^{10^3}=x$

    $\displaystyle x^{\log_2x}=32x^4\Longrightarrow \log_2\left(x^{\log_2x}\right)=\log_2\left(32x^4\r ight)\Longrightarrow $ $\displaystyle \log_xx\cdot\log_2x=5+4\log_2x$ ...you finish the argument.

    Of course, you must know VERY WELL the definition and properties of logarithms to prove the above.

    Tonio
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