simplify ln(e(1/5))

Solution

simplify

ln (e (\frac{1}{5}))

ln (e) + + ln (1) - ln (5)

Decimal Notation

- 0.60943 \dots

Solution steps

ln (e (\frac{1}{5}))

Apply log rule:

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

ln (e (\frac{1}{5})) = ln (e) + ln (\frac{1}{5})

= ln (e) + ln (\frac{1}{5})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1}{5}) = ln (1) - ln (5)

= ln (e) + + ln (1) - ln (5)

- 3 ln (x) - 3 ln (y)

\frac{1}{2} [ln (x + 1) + 2 ln (x - 1)] + 3 ln (x)

ln ((e^{3}) \cdot (x^{3}) \cdot (y^{4}))

\frac{5}{4} ln (x) - \frac{7}{2 x} - \frac{5}{4} ln (x + 2) + C

lo g_{10} ((tan (x))^{\circ}) 2 x