if x=log 3 base2 and Y= log 5base2 then express log 60base 2 in x ,y terms
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Answer:
log
2
(7.5)=log
2
(15÷2)
=>log
2
(15)−log
2
(2)
=>log
2
(5×3)−1
=>log
2
(5)+log
2
(3)−1
=>y+x−1
6750 = {5}^{3} \times {3}^{3} \times 26750=5
3
×3
3
×2
take logarithm with Base 2 in both sides
\begin{gathered} log_{2}(6750) = log_{2}( {5}^{3} \times {3}^{3} \times 2) \\ = log_{2}( {5}^{3} ) + log_{2}( {3}^{3} ) + log_{2}(2) \\ = 3 log_{2}(5) + 3 log_{2}(3) + 1 \\ = 3y + 3x + 1\end{gathered}
log
2
(6750)=log
2
(5
3
×3
3
×2)
=log
2
(5
3
)+log
2
(3
3
)+log
2
(2)
=3log
2
(5)+3log
2
(3)+1
=3y+3x+1
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