simplify ln(2*e^x)

Solution

simplify

ln (2 \cdot e^{x})

ln (2) + x

Solution steps

ln (2 e^{x})

Apply log rule:

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

ln (2 e^{x}) = ln (2) + ln (e^{x})

= ln (2) + ln (e^{x})

Apply log rule:

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

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

= ln (2) + x ln (e)

x ln (e) = x

= ln (2) + x

ln (\frac{x x ^{3} - 1}{x ^{5} + 9})

\frac{1}{2} lo g_{c} (x) + 4 lo g_{c} (y) - 5 lo g_{c} (x)

lo g_{3} (\frac{2 x - 1}{5 x + 2})

lo g_{10} (\frac{6 w ^{5}}{x})

ln (\frac{729}{10000})