simplify ln(e^y*y)

Solution

simplify

ln (e^{y} \cdot y)

y + ln (y)

Solution steps

ln (e^{y} y)

Apply log rule:

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

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

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

Apply log rule:

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

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

= y ln (e) + ln (y)

y ln (e) = y

= y + ln (y)

ln (x) - 3 ln (y) - 4 ln (z)

ln (\frac{24}{1079})

ln (x - 2) [ln (x - 5) + ln (x + 5)]

lo g_{10} (\frac{3.08}{1.42}) - 1

- ln (\frac{5}{4}) + 4