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Popular >

simplify ln(a*e^{-x/5})

Solution

simplify

ln (a \cdot e^{- \frac{x}{5}})

Solution

ln (a) - \frac{x}{5}

Solution steps

ln (a e^{- \frac{x}{5}})

Apply log rule:

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

ln (a e^{- \frac{x}{5}}) = ln (a) + ln (e^{- \frac{x}{5}})

= ln (a) + ln (e^{- \frac{x}{5}})

Apply log rule:

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

ln (e^{- \frac{x}{5}}) = - \frac{x}{5} ln (e)

= ln (a) - \frac{x}{5} ln (e)

\frac{x}{5} ln (e) = \frac{x}{5}

= ln (a) - \frac{x}{5}

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Frequently Asked Questions (FAQ)

What is ln(a*e^{-x/5}) ?
The solution to ln(a*e^{-x/5}) is ln(a)-x/5