What is simplify-4/8 ln(4/8)-4/8 ln(4/8) ?

The solution to simplify-4/8 ln(4/8)-4/8 ln(4/8) is ln(2)

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simplify-4/8 ln(4/8)-4/8 ln(4/8)

simplify

- \frac{4}{8} ln (\frac{4}{8}) - \frac{4}{8} ln (\frac{4}{8})

ln (2)

Decimal

0.69314 \dots

Solution steps

- \frac{4}{8} ln (\frac{4}{8}) - \frac{4}{8} ln (\frac{4}{8})

Apply log rule:

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

ln (\frac{4}{8}) = ln (4) - ln (8), ln (\frac{4}{8}) = ln (4) - ln (8)

= - \frac{4}{8} (ln (4) - ln (8)) - \frac{4}{8} (ln (4) - ln (8))

Add similar elements:

- \frac{4}{8} (ln (4) - ln (8)) - \frac{4}{8} (ln (4) - ln (8)) = - (ln (4) - ln (8))

= - (ln (4) - ln (8))

ln (4) = 2 ln (2)

ln (8) = 3 ln (2)

= - (2 ln (2) - 3 ln (2))

Add similar elements:

2 ln (2) - 3 ln (2) = - ln (2)

= - (- ln (2))

Apply rule

- (- a) = a

= ln (2)

- lo g_{10} (3.9 (1 0^{- 8}))

lo g_{10} \frac{( b ^{3} )}{a ^{5} c ^{8}}

ln (2 n^{3} + 2) - ln (5 n^{3} + 2 n^{2} + 4)

2 ln (t) + ln^{2} (t)

4 - \frac{5}{2} ln (5) - \frac{11}{8} + \frac{5}{2} ln (2)

What is simplify-4/8 ln(4/8)-4/8 ln(4/8) ?
The solution to simplify-4/8 ln(4/8)-4/8 ln(4/8) is ln(2)