simplify ln(2e^2)

Solution

simplify

ln (2 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{x}{x - 7}) + ln (\frac{x + 7}{x}) - ln (x^{2} - 49)

- (\frac{9}{14}) lo g_{2} (\frac{9}{14}) - (\frac{5}{14}) lo g_{2} (\frac{5}{14})

lo g_{10} (\frac{x y ^{7}}{z ^{3}})

ln (x) - ln (x + 1)