simplify ln(3e^2)

Solution

simplify

ln (3 e^{2})

ln (3) + 2

Decimal Notation

3.09861 \dots

Solution steps

ln (3 e^{2})

Apply log rule:

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

ln (3 e^{2}) = ln (3) + ln (e^{2})

= ln (3) + ln (e^{2})

Apply log rule:

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

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

= ln (3) + 2 ln (e)

2 ln (e) = 2

= ln (3) + 2

lo g_{b} (x^{2} y)

- lo g_{10} (2 \cdot 1 0^{- 4})

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

3 lo g_{10} (x) + 2 lo g_{10} (y)

lo g_{5} (8) - lo g_{5} (t)