simplify ln(2e^4)

Solution

simplify

ln (2 e^{4})

ln (2) + 4

Decimal Notation

4.69314 \dots

Solution steps

ln (2 e^{4})

Apply log rule:

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

ln (2 e^{4}) = ln (2) + ln (e^{4})

= ln (2) + ln (e^{4})

Apply log rule:

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

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

= ln (2) + 4 ln (e)

4 ln (e) = 4

= ln (2) + 4

ln (\frac{e}{11})

ln (\frac{a - x}{a + x})

\frac{3}{2} ln (x^{6}) - \frac{3}{4} ln (x^{8})

lo g_{10} (9 x^{2})

lo g_{3} (9 x^{5})