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) * {7}^(2) * 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 \: (3)/(2) log_(2)(2) + (2)/(2) log_(2)(7) - (1)/(2) log_(2)(10)`

`\qquad \sf  \dashrightarrow \: (3)/(2) + a - (b)/(2)`

That's the required result ~

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

`\qquad \sf  \dashrightarrow \: (2a - b + 3)/(2)`