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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

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Frequently Asked Questions (FAQ)

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