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

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

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

simplify

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

\frac{ln ( 2 )}{2}

Solution steps

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

Apply log rule:

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

1 \cdot (ln (2) - ln (4)) = ln (2) - ln (4)

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

Subtract the numbers:

2 - 4 = - 2

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

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

ln (2) - ln (4) = - (ln (4) - ln (2))

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

ln (4) = 2 ln (2)

= \frac{2 ln ( 2 ) - ln ( 2 )}{2}

Add similar elements:

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

= \frac{ln ( 2 )}{2}

5 lo g_{3} (x) + 3 lo g_{3} (y)

ln (\frac{40}{11})

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ln (x) + ln (1 + x)