What is ln(ae^{-b/c}) ?

The solution to ln(ae^{-b/c}) is ln(a)-b/c

Popular >

simplify ln(ae^{-b/c})

simplify

ln (a e^{- \frac{b}{c}})

ln (a) - \frac{b}{c}

Solution steps

ln (a e^{- \frac{b}{c}})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (a e^{- \frac{b}{c}}) = ln (a) + ln (e^{- \frac{b}{c}})

= ln (a) + ln (e^{- \frac{b}{c}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{- \frac{b}{c}}) = - \frac{b}{c} ln (e)

= ln (a) - \frac{b}{c} ln (e)

\frac{b}{c} ln (e) = \frac{b}{c}

= ln (a) - \frac{b}{c}

\frac{1}{2} ln (3) + \frac{3}{2} ln (2)

ln (\frac{x}{x - 1}) + ln (\frac{x + 1}{x})

ln (\frac{3}{22})

\frac{- ( \frac{y}{x} ) ^{2}}{2} + \frac{8}{7} \frac{y}{x} - \frac{3}{7} ln (\frac{y}{x})

8.07428 ln \frac{P}{( P - 90 )} - 8.07428 ln (\frac{4}{41})