Question

if log7=a and log…
help me solve ths math problem on picture

Answer 1

$\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}$

Let's solve ~

$\qquad \sf  \dashrightarrow \: log_{4}(39.2)$

$\qquad \sf  \dashrightarrow \: log_{4}( {2}^{3} \times {7}^{2} \times 10 {}^{ - 1} )$

$\qquad \sf  \dashrightarrow \: log_{4}( {2}^{3} ) + log_{4}( {7}^{2} ) + log_{4}(10 {}^{ - 1} )$

$\qquad \sf  \dashrightarrow \: log_{ {2}^{2} }( {2}^{3} ) + log_{ {2}^{2} }( {7}^{2} ) + log_{ {2}^{2} }(10 {}^{ - 1} )$

$\qquad \sf  \dashrightarrow \: \frac{3}{2} log_{2}(2) + \frac{2}{2} log_{2}(7) - \frac{1}{2} log_{2}(10)$

$\qquad \sf  \dashrightarrow \: \frac{3}{2} + a - \frac{b}{2}$

That's the required result ~

also you can take it's LCM and write it as :

$\qquad \sf  \dashrightarrow \: \dfrac{2a - b + 3}{2}$