Rewrite the logarithm as a ratio of (a) common logarithms and (b) natural logarithms. log5 x

FizeauV

FizeauV

Answered question

2020-11-20

Rewrite the logarithm as a ratio of
(a) common logarithms and
(b) natural logarithms. log5x

Answer & Explanation

Tasneem Almond

Tasneem Almond

Skilled2020-11-21Added 91 answers

To evaluate logarithms to any base, we use the change-of-base formula: logca=logbalogbc
a) log5x=logxlog5
This is a common logarithm as the base is changed from 5 to 10 the same way the logarithm is changed from base “c” to base “b” in the formula.
b) log5x=lnxln5
To change log5 x to ratio of a natural logarithm, change log5, also written as ln.

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