simplify ln(x*e^y)

Solution

simplify

ln (x \cdot e^{y})

ln (x) + y

Solution steps

ln (x e^{y})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (x) + y ln (e)

y ln (e) = y

= ln (x) + y

lo g_{10} (\frac{y}{1})

ln (\frac{1 - 1 - 4 x ^{2}}{2 x})

- lo g_{10} (1.34 \cdot 1 0^{- 3})

lo g_{3} (4) + lo g_{3} (11)

lo g_{10} (6) + 4 lo g_{10} (2)