What is 1/3 ln((1/2)/(3/4)) ?

The solution to 1/3 ln((1/2)/(3/4)) is 1/3 (-ln(2)-ln(3/4))

Popular >

simplify 1/3 ln((1/2)/(3/4))

simplify

\frac{1}{3} ln (\frac{\frac{1}{2}}{\frac{3}{4}})

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

Decimal Notation

- 0.13515 \dots

Solution steps

\frac{1}{3} ln (\frac{\frac{1}{2}}{\frac{3}{4}})

Apply log rule:

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

ln (\frac{\frac{1}{2}}{\frac{3}{4}}) = ln (\frac{1}{2}) - ln (\frac{3}{4})

= \frac{1}{3} (ln (\frac{1}{2}) - ln (\frac{3}{4}))

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= \frac{1}{3} (- ln (2) - ln (\frac{3}{4}))

8 lo g_{b} (x) + 7 lo g_{b} (z)

\frac{π}{8} ln (\frac{13}{5})

- [\frac{2}{6} lo g_{2} (\frac{2}{6}) + \frac{4}{6} lo g_{2} (\frac{4}{6})]

3 lo g_{b} (q) - lo g_{b} (r)

lo g_{2} ((3^{6} \cdot 7)^{4})

What is 1/3 ln((1/2)/(3/4)) ?
The solution to 1/3 ln((1/2)/(3/4)) is 1/3 (-ln(2)-ln(3/4))