simplify ln(e/(13))

Solution

simplify

ln (\frac{e}{13})

1 - ln (13)

Decimal Notation

- 1.56494 \dots

Solution steps

ln (\frac{e}{13})

Apply log rule:

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

ln (\frac{e}{13}) = ln (e) - ln (13)

= ln (e) - ln (13)

Apply log rule:

lo g_{a} (a) = 1

= 1 - ln (13)

lo g_{10} (\frac{x}{1000 y ^{6}})

lo g_{2} (\frac{x ^{3} y ^{8}}{5})

\frac{ln ( x )}{2} - 4 ln (y) - \frac{1}{3} ln (x + 2)

- \frac{1}{2} + \frac{1}{4} lo g_{10} (0.1) + \frac{1}{2} lo g_{10} (a)

ln (9) + ln (x)