simplify ln(e^2x)

Solution

simplify

ln (e^{2} x)

2 + ln (x)

Solution steps

ln (e^{2} x)

Apply log rule:

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

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

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

Apply log rule:

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

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

= 2 ln (e) + ln (x)

2 ln (e) = 2

= 2 + ln (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)

2 ln (x) - \frac{1}{2} ln (y)