simplify ln(ye^y)

Solution

simplify

ln (y e^{y})

ln (y) + y

Solution steps

ln (y e^{y})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (y) + y ln (e)

y ln (e) = y

= ln (y) + y

- lo g_{2} (7) + 2 lo g_{2} (x)

ln (\frac{e ^{3}}{7})

lo g_{3} (\frac{3 y ^{4}}{y x})

\frac{5}{2} lo g_{10} (x) - lo g_{10} (y)

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