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

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

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

simplify

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

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

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

Apply log rule:

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

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

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

Multiply fractions:

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

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

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

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

Subtract the numbers:

1 - 2 = - 1

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

Apply the fraction rule:

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

ln (1) - ln (2) = - (ln (2) - ln (1))

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

Apply rule

\frac{a}{1} = a

= ln (2) - ln (1)

Apply log rule:

lo g_{a} (1) = 0

= ln (2) - 0

ln (2) - 0 = ln (2)

= ln (2)

ln (x^{12} 4 - x)

50 \cdot ln (\frac{54.8}{72})

- lo g_{10} (3.89 \cdot 1 0^{- 4})

ln (x + 1) + ln (x - 1)

ln (x) - \frac{1}{2} ln (x^{2} + 1)