Question

if log 3= a, log4=b, log 72=？

Answer 1

$Given \: log \: 3 = a \: --(1)$

$log \: 4 = b$

$\implies log \: 2^{2} = b$

$\implies 2 log \: 2= b$

$\implies log \: 2= \frac{b}{2} \: --(2)$

$Now, Value \: of \: log \: 72$

$= log \: (8 \times 9)$

$= log \: 8 + log \: 9$

$= log \: 2^{3} + log \: 3^{2}$

$= 3 log 2 + 2 log 3$

$= 3 \times \frac{b}{2} + 2 \times a$

$= \frac{3b}{2} + 2 a$

Therefore.,

$\red{ Value \: of \: log \: 72}$

$\green { = \frac{3b}{2} + 2 a}$

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