f-p-2-qr-prove-thathat-log-r-p-log-q-p-2log-q-p-log-r-p-

Question Number 17748 by ibraheem160 last updated on 10/Jul/17

f p^{2} = q r, p r o v e t h a t h a t {l o g}_{r}^{p} + {l o g}_{q =}^{p}

2 {l o g}_{q}^{p} {l o g}_{r}^{p}

Commented by tawa tawa last updated on 10/Jul/17

\frac{logp}{logr} + \frac{logp}{logq}

= \frac{logplogq + logplogr}{logrlogq}

= \frac{logp [logq + logr]}{logrlogq}

= \frac{logp (logqr)}{logrlogq}

from p^{2} = qr

= \frac{{logplogp}^{2}}{logrlogq}

= \frac{logp}{logr} \times \frac{{logp}^{2}}{logq}

= \log_{r} p \times {2 \log}_{q} p

= {2 \log}_{q} {plog}_{r} p

QED