Express $${{log}}_{{\mathtt{7}}}{\left({\mathtt{4}}\right)}$$ in terms of natural logaritms. Do not find a numerical answer.
+33615 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)
+33615 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)
