Write \log_218x^2y^{5^2} as a sum of logarithms. Express powers as

Payton Benson

Payton Benson

Answered question

2022-03-09

Write log218x2y52 as a sum of logarithms. Express powers as factors.

Answer & Explanation

Pamela Browning

Pamela Browning

Beginner2022-03-10Added 1 answers

Given, log218x2y52.
Apply log rule: logc(ab)=logc(a)+logc(b)
log218x2y52=log2(18)+log2(x2)+log2(y52)
Apply log rule: loga(xb)=bloga(x)
log2(18)+log2(x2)+log2(y52)=log2(18)+2log2(x)+52log2(y)
Finally, simplifying
log2(18)+2log2(x)+52log2(y)=log2(18)+2log2(x)+25log2(y)
This is the required answer.

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