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Gemiola [76]
2 years ago
13

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

Mathematics
1 answer:
tatiyna2 years ago
3 0

\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}

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