simplify ln(5e^3)

Solution

simplify

ln (5 e^{3})

ln (5) + 3

Decimal Notation

4.60943 \dots

Solution steps

ln (5 e^{3})

Apply log rule:

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

ln (5 e^{3}) = ln (5) + ln (e^{3})

= ln (5) + ln (e^{3})

Apply log rule:

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

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

= ln (5) + 3 ln (e)

3 ln (e) = 3

= ln (5) + 3

- lo g_{10} (2.3 \cdot 1 0^{- 7})

ln (\frac{x ^{8} x ^{2} + 2}{( x + 2 ) ^{9}})

- lo g_{10} (8.4 \cdot 1 0^{- 11})

ln \frac{x + 5}{2} + 1 - ln \frac{x + 5}{2} - 1

ln (\frac{8}{6})