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Thread: Help me with log. tmr exam!

  1. Mar 25th 2009, 12:15 AM #1
    helloying
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    Help me with log. tmr exam!

    lgx+ln2x=3
    solve the eqn
    thanks
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  2. Mar 25th 2009, 03:54 AM #2
    Grandad
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    Hello helloying
    Quote Originally Posted by helloying View Post
    lgx+ln2x=3
    solve the eqn
    thanks
    I assume that lgx means \log_{10}x and ln2x means \log_e2x (= \log_e2 + \log_ex).

    In which case, you need to know that \log_{10}x = \frac{\log_ex}{\log_e10}. So the equation becomes:

    \frac{\log_ex}{\log_e10} + \log_e2 + \log_ex = 3

    \Rightarrow \log_ex\left(\frac{1}{\log_e10} + 1\right)= 3 - \log_e2

    Can you finish it from here?

    Grandad
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