simplify ln(a*e^x)

Solution

simplify

ln (a \cdot e^{x})

ln (a) + x

Solution steps

ln (a e^{x})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (a) + x ln (e)

x ln (e) = x

= ln (a) + x

3 lo g_{a} (x) - \frac{1}{4} lo g_{a} (w) + 7 lo g_{a} (y)

- ln (7 e^{- x})

3 ln (pq) + 4 ln (p q^{2})

lo g_{e} (\frac{5204}{5101})

lo g_{10} (2 π \cdot 802 \cdot 5.03 \cdot 9.566)