simplify ln(e^xf)

Solution

simplify

ln (e^{x} f)

x + ln (f)

Solution steps

ln (e^{x} f)

Apply log rule:

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

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

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

Apply log rule:

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

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

= x ln (e) + ln (f)

x ln (e) = x

= x + ln (f)

ln (\frac{x ^{9} x ^{2} + 7}{( x + 7 ) ^{4}})

ln (7) - 3 ln (x)

ln (2.01 \cdot 1 0^{- 2})

\frac{1}{2} lo g_{7} (x) + \frac{1}{2} lo g_{7} (y)

ln (\frac{h}{a})