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Thread: Arithematic Progression -Logarithm

  1. #1
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    Arithematic Progression -Logarithm

    If $\displaystyle log_k x, log_m x , log_nx$ are in A.P then prove that $\displaystyle n^2 = (kn)^{log_km}$

    If the terms are in A.P then : $\displaystyle 2 log_mx = log_k x + log_nx = \frac{2}{log_xm} = \frac{1}{log_xk}+ \frac{1}{log_xn}$

    =$\displaystyle \frac{2}{log_xm}= \frac{log_xn+log_xk}{log_xklog_xn}$ can we solve this way or not..............please guide
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  2. #2
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    Re: Arithematic Progression -Logarithm

    $\displaystyle 2\log_{m}x = \log_{k}x + \log_{n}x.$

    Start by using the change of base formula so that all logs are to base $\displaystyle k.$

    Cancel the $\displaystyle \log_{k}x$ throughout, cross multiply and that gets you a $\displaystyle 2\log_{k}n$ (which becomes) $\displaystyle \log_{k}n^2$ on the LHS.

    Try finishing from there.
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  3. #3
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    Re: Arithematic Progression -Logarithm

    thanks a lot....i got it..regards,sachin
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