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Express $${{log}}_{{\mathtt{7}}}{\left({\mathtt{4}}\right)}$$ in terms of natural logaritms. Do not find a numerical answer.

Guest May 29, 2014

#1
+26716
+5

Let x = log7(4)

This means that

7x = 4

Take the natural log of both sides (ln means log to base e)

ln(7x) = ln(4)

By a property of logarithms (see the Formulary at the top of this page) we have

x*ln(7) = ln(4)

so x = ln(4)/ln(7) or, substituting for x from the first line above):

log7(4) = ln(4)/ln(7)

Alan  May 29, 2014
#1
+26716
+5

Let x = log7(4)

This means that

7x = 4

Take the natural log of both sides (ln means log to base e)

ln(7x) = ln(4)

By a property of logarithms (see the Formulary at the top of this page) we have

x*ln(7) = ln(4)

so x = ln(4)/ln(7) or, substituting for x from the first line above):

log7(4) = ln(4)/ln(7)

Alan  May 29, 2014