simplify ln(9e^x)

Solution

simplify

ln (9 e^{x})

2 ln (3) + x

Solution steps

ln (9 e^{x})

Apply log rule:

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

ln (9 e^{x}) = ln (9) + ln (e^{x})

= ln (9) + ln (e^{x})

Apply log rule:

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

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

= ln (9) + x ln (e)

x ln (e) = x

= ln (9) + x

ln (9) = 2 ln (3)

= 2 ln (3) + x

2 (lo g_{6} (x) + 2 lo g_{6} (y) - 3 lo g_{6} (z))

\frac{1}{3} (3 ln (x + 4) + ln (x) - ln (x^{2} - 5))

2 lo g_{x} (- 3 lo g_{y} (+ 4 lo g_{z} (x)))

lo g_{10} (\frac{y ^{5}}{z ^{2} x ^{3}})

4 ln (x) + 2 ln (y)