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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

Best Answer 

 #1
avatar+26402 
+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
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1+0 Answers

 #1
avatar+26402 
+5
Best Answer

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

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