simplify ln(0.3e^4)

Solution

simplify

ln (0.3 e^{4})

ln (0.3) + 4

Decimal Notation

2.79602 \dots

Solution steps

ln (0.3 e^{4})

Apply log rule:

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

ln (0.3 e^{4}) = ln (0.3) + ln (e^{4})

= ln (0.3) + ln (e^{4})

Apply log rule:

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

ln (e^{4}) = 4 ln (e)

= ln (0.3) + 4 ln (e)

4 ln (e) = 4

= ln (0.3) + 4

2 ln (5 x^{3}) + ln (2 x^{2})

ln (\frac{\frac{1}{2}}{0.144})

\frac{25 ln ( 3 ) - 9 ln ( 5 )}{8} + 1

\frac{1}{144} ln (2)

ln (x^{8} 7 - x)