simplify ln(5e^2)

Solution

simplify

ln (5 e^{2})

ln (5) + 2

Decimal Notation

3.60943 \dots

Solution steps

ln (5 e^{2})

Apply log rule:

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

ln (5 e^{2}) = ln (5) + ln (e^{2})

= ln (5) + ln (e^{2})

Apply log rule:

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

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

= ln (5) + 2 ln (e)

2 ln (e) = 2

= ln (5) + 2

lo g_{10} (z^{5} x^{3} y)

lo g_{10} (\frac{p q ^{3}}{s})

lo g_{10} (\frac{c ^{6}}{a b ^{3}})

lo g_{b} (4) + lo g_{b} (3)

lo g_{6} (\frac{36 a ^{6} 1 - b}{c ( b + 5 ) ^{2}})