simplify ln(-ae^x)

Solution

simplify

ln (- a e^{x})

ln (a) + x

Solution steps

ln (- a e^{x})

Apply log rule:

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

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

= ln (a) + ln (e^{x})

Apply log rule:

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

ln (e^{x}) = x ln (e)

= ln (a) + x ln (e)

x ln (e) = x

= ln (a) + x

- lo g_{10} (5.3 \cdot 1 0^{- 7})

\frac{1}{99999999} ln (10)

5 (2 ln (6) - 1 - ln (3))

ln (\frac{201.3}{201.2})

ln (24 + 2) + ln (52)