simplify ln(ex^2)

Solution

simplify

ln (e x^{2})

1 + 2 ln (x)

Solution steps

ln (e x^{2})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (e) + 2 ln (x)

Apply log rule:

lo g_{a} (a) = 1

= 1 + 2 ln (x)

ln ((θ + 1)^{n} \cdot (x^{θ}))

ln (7) 7

- lo g_{10} (1.541 \cdot 1 0^{- 5})

\frac{1}{3} ln (100) + \frac{2}{3} ln (200)