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

Guest May 29, 2014

#1**+5 **

Let x = log_{7}(4)

This means that

7^{x} = 4

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

ln(7^{x}) = 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):

log_{7}(4) = ln(4)/ln(7)

Alan
May 29, 2014

#1**+5 **

Best Answer

Let x = log_{7}(4)

This means that

7^{x} = 4

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

ln(7^{x}) = 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):

log_{7}(4) = ln(4)/ln(7)

Alan
May 29, 2014