What is ln(1/a e^{-x/a}) ?

The solution to ln(1/a e^{-x/a}) is -x/a-ln(a)

Popular >

simplify ln(1/a e^{-x/a})

simplify

ln (\frac{1}{a} e^{- \frac{x}{a}})

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

Solution steps

ln (\frac{1}{a} e^{- \frac{x}{a}})

Apply log rule:

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

ln (\frac{1}{a} e^{- \frac{x}{a}}) = ln (\frac{1}{a}) + ln (e^{- \frac{x}{a}})

= ln (\frac{1}{a}) + ln (e^{- \frac{x}{a}})

Apply log rule:

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

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

= ln (\frac{1}{a}) - \frac{x}{a} ln (e)

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1}{a}) = ln (1) - ln (a)

= ln (1) - ln (a) - ln (e) \frac{x}{a}

ln (1) = 0

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

= 0 - ln (a) - \frac{x}{a}

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

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

8 lo g_{e} (2 x) - lo g_{e} (2)

lo g_{2} ((x^{3} + 2) (x - 4)^{3})

lo g_{10} (5 \cdot 1 0^{- 3})

ln ((x + 1)^{2} m)

ln (2 n) + 3 ln (b) n - ln (π) n - 2 ln (b^{2} + (x - a)^{2})