simplify ln(Ae^7)

Solution

simplify

ln (A e^{7})

ln (A) + 7

Solution steps

ln (A e^{7})

Apply log rule:

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

ln (A e^{7}) = ln (A) + ln (e^{7})

= ln (A) + ln (e^{7})

Apply log rule:

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

ln (e^{7}) = 7 ln (e)

= ln (A) + 7 ln (e)

7 ln (e) = 7

= ln (A) + 7

3 ln (2 e^{2 x}) + 2 ln (e^{- 3 x})

ln (10) + ln (7)

ln (x - 1) + ln (x + 1)

ln (\frac{sin ( x )}{1 + cos ( x )})

ln (x) - 8 [ln (x - 2) + ln (x + 2)]