How to simplify \(\displaystyle{\frac{{{{\log}_{{2}}{625}}}}{{{{\log}_{{2}}{125}}}}}\)

Alessandra Carrillo

Alessandra Carrillo

Answered question

2022-04-09

How to simplify log2625log2125

Answer & Explanation

prangijahnot

prangijahnot

Beginner2022-04-10Added 17 answers

Without a change of base:
log2625log2125=log2(54)log2(53)=4log253log25=43.
cadhail6n1t

cadhail6n1t

Beginner2022-04-11Added 14 answers

log2625log2125=log125625=log5625log5125=log554log553=43
by virtue of a basic property of logarithms. The basic property I am referring to is the following:
logaxlogay=logyx

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