simplify ln(2e^3)

Solution

simplify

ln (2 e^{3})

ln (2) + 3

Decimal Notation

3.69314 \dots

Solution steps

ln (2 e^{3})

Apply log rule:

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

ln (2 e^{3}) = ln (2) + ln (e^{3})

= ln (2) + ln (e^{3})

Apply log rule:

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

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

= ln (2) + 3 ln (e)

3 ln (e) = 3

= ln (2) + 3

ln (e^{2} x)

ln (\frac{x ^{3} y ^{2}}{z ^{5}})

ln (2 a) - ln (a)

lo g_{10} (\frac{x ^{3}}{y ^{4}})

lo g_{10} (x) + 5 lo g_{10} (y) - 4 lo g_{10} (z)