simplify ln(ye^x)

Solution

simplify

ln (y e^{x})

ln (y) + x

Solution steps

ln (y e^{x})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (y) + x ln (e)

x ln (e) = x

= ln (y) + x

- lo g_{10} (4.5 \cdot 1 0^{- 4})

ln (\frac{x ^{2}}{x ( 1 + x ) ^{5}})

lo g_{2} (8 x y)

lo g_{\frac{1}{6}} (\frac{4}{9})

- \frac{6}{8} lo g_{2} (\frac{6}{8}) - \frac{2}{8} lo g_{2} (\frac{2}{8})