Question-197125

Question Number 197125 by Amidip last updated on 08/Sep/23

Commented by som(math1967) last updated on 08/Sep/23

b = ?

Answered by Frix last updated on 09/Sep/23

a = \frac{\ln 18}{\ln 12} = \frac{2 \ln 3 + \ln 2}{\ln 3 + 2 \ln 2} = \frac{2 p + q}{p + 2 q}

b = \frac{\ln 54}{\ln 24} = \frac{3 \ln 3 + \ln 2}{\ln 3 + 3 \ln 2} = \frac{3 p + q}{p + 3 q}

a b + 5 (a - b) =

= \frac{6 p^{2} + 5 p q + q^{2}}{(p + 2 q) (p + 3 q)} - \frac{5 (p^{2} - q^{2})}{(p + 2 q) (p + 3 q)} =

= \frac{p^{2} + 5 p q + 6 q^{2}}{(p + 2 q) (p + 3 q)} = \frac{(p + 2 q) (p + 3 q)}{(p + 2 q) (p + 3 q)} = 1

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