Given log3 4=1.262 and log3 7=1.771, what is the value of log3 (16/7)?

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asked Jan 18, 2023 37.2k views

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Given log3 4=1.262 and log3 7=1.771, what is the value of log3 (16/7)?

Mathematics
high-school

Ankita Kuchhadiya asked

by Ankita Kuchhadiya

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1 Answer

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Answer:

Explanation:

$log (a)/(b)=log \ a - log \ b\\\\log \ a^(m)=m*log \ a\\\\\\log_(3) \ (16)/(7)=log_(3) \ 16 - log_(3) \ 7\\\\\\= log_(3) \ 4^(2) - log_(3) \ 7\\\\=2*log_(3) \ 4 - log_(3) \ 7\\\\= 2 * 1.262 - 1.771\\\\= 2.524 - 1.771\\\\= 0.753$

Yuwen answered Jan 22, 2023

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