What is 1/2-1/3 (ln(2)-ln(8)-ln(1)+ln(5)) ?

The solution to 1/2-1/3 (ln(2)-ln(8)-ln(1)+ln(5)) is 1/2-1/3 ln(5/4)

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simplify 1/2-1/3 (ln(2)-ln(8)-ln(1)+ln(5))

simplify

\frac{1}{2} - \frac{1}{3} (ln (2) - ln (8) - ln (1) + ln (5))

\frac{1}{2} - \frac{1}{3} ln (\frac{5}{4})

Decimal Notation

0.42561 \dots

Solution steps

\frac{1}{2} - \frac{1}{3} (ln (2) - ln (8) - ln (1) + ln (5))

Apply log rule:

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

ln (5) - ln (8) = ln (\frac{5}{8})

= \frac{1}{2} - \frac{1}{3} (ln (2) + ln (\frac{5}{8}) - ln (1))

Apply log rule:

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

ln (2) + ln (\frac{5}{8}) = ln (2 \cdot \frac{5}{8})

= \frac{1}{2} - \frac{1}{3} (ln (2 \cdot \frac{5}{8}) - ln (1))

2 \cdot \frac{5}{8} = \frac{5}{4}

= \frac{1}{2} - \frac{1}{3} (ln (\frac{5}{4}) - ln (1))

\frac{1}{3} (ln (\frac{5}{4}) - ln (1)) = \frac{1}{3} ln (\frac{5}{4})

= \frac{1}{2} - \frac{1}{3} ln (\frac{5}{4})

ln (x) - ln (y) + 1

8 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

- 2.48 ln (\frac{0.67}{1.33})

ln (\frac{u - a}{u + a})

ln (2) \cdot \frac{π}{3}

What is 1/2-1/3 (ln(2)-ln(8)-ln(1)+ln(5)) ?
The solution to 1/2-1/3 (ln(2)-ln(8)-ln(1)+ln(5)) is 1/2-1/3 ln(5/4)