simplify ln(2*e^2)

Solution

simplify

ln (2 \cdot e^{2})

ln (2) + 2

Decimal Notation

2.69314 \dots

Solution steps

ln (2 e^{2})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (2) + 2 ln (e)

2 ln (e) = 2

= ln (2) + 2

ln (\frac{19.1086}{18.3112})

3 ln (- 1) - 3 ln (- 2)

ln (9.68 \cdot 1 0^{- 3})

3 ln (1) - 3 ln (\frac{3}{2})

ln (\frac{6.8}{7})