simplify ln(10e^2)

Solution

simplify

ln (10 e^{2})

ln (10) + 2

Decimal Notation

4.30258 \dots

Solution steps

ln (10 e^{2})

Apply log rule:

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

ln (10 e^{2}) = ln (10) + ln (e^{2})

= ln (10) + ln (e^{2})

Apply log rule:

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

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

= ln (10) + 2 ln (e)

2 ln (e) = 2

= ln (10) + 2

\frac{1}{2} lo g_{10} (s) + 5 lo g_{10} (x)

- lo g_{10} (1.4 \times 1 0^{- 3})

lo g_{2} (\frac{x ^{4}}{2 y})

ln (r i g h t)

lo g_{b} (b^{13}) + lo g_{b} (1)