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   3 logp q + 2 logq p = 7    for q > p > 1

log q          log p2

——-   +       ———-         =     7

 log p             log q

3(log q) + 2 (log p)2

————————-       =     7

      log p log q

3(log q) + 2 (log p)2     = 7 log p log q

3(log q)  – 7 log p log q  + 2 (log p) = 0

( 3log q – log p) (log q – 2log p) = 0

3log q = log p                 and/or             log q  = 2log p

log q = (1/3) log p                                   log q = log p 

log q = log p1/3

=> q = p1/3                                             => q = p

Given  q > p > 1,

=>  q = p1/3   is extraneous because say, if p = 8, q = 2  => q < p

       So  q = p  because it satisfies the condition  q > p > 1

1 Reply 1 Like

I never knew the power of converting bases until now… 😍

1 Reply 0 Likes

The power of Math is so beautiful right?    Most people don’t realise it.

Math is a wonderful sanctuary where all problems can be solved, except only if wrongly set.    lol

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