simplify ln(3e^4)

Solution

simplify

ln (3 e^{4})

ln (3) + 4

Decimal Notation

5.09861 \dots

Solution steps

ln (3 e^{4})

Apply log rule:

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

ln (3 e^{4}) = ln (3) + ln (e^{4})

= ln (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 (3) + 4 ln (e)

4 ln (e) = 4

= ln (3) + 4

ln (\frac{s ^{2} + 16}{s ^{2} + 64})

ln (\frac{12}{5})

ln (x) + 2 ln (y) - 3 ln (z)

2 ln (x) + ln (x + 1)

\frac{1}{2} ln (x) + 7 ln (y) - 3 ln (w)