simplify ln(xe^2)

Solution

simplify

ln (x e^{2})

ln (x) + 2

Solution steps

ln (x e^{2})

Apply log rule:

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

ln (x e^{2}) = ln (x) + ln (e^{2})

= ln (x) + ln (e^{2})

Apply log rule:

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

ln (e^{2}) = 2 ln (e)

= ln (x) + 2 ln (e)

2 ln (e) = 2

= ln (x) + 2

\frac{1}{2} ln ∣ x ∣ - 2 ln 1 - x

lo g_{10} (14.22) + lo g_{10} (0.11)

- lo g_{10} (8.5 x 1 0^{- 6})

10 lo g_{6} (c) + 10 lo g_{6} (a) - 2 lo g_{6} (b)

\frac{3}{5} \cdot (- \frac{2}{3} lo g_{e} (\frac{2}{3}) - \frac{1}{3} lo g_{e} (\frac{1}{3}))