Arithematic Progression -Logarithm

**sachinrajsharma** · February 27th 2013, 07:43 AM

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

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

= $\frac{2}{log_xm}= \frac{log_xn+log_xk}{log_xklog_xn}$ can we solve this way or not..............please guide

**BobP** · February 27th 2013, 12:36 PM

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

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

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

Try finishing from there.

**sachinrajsharma** · February 27th 2013, 06:20 PM

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

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