What is 1/2 ln(1/2)+1/2 ln(1/2) ?

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

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simplify 1/2 ln(1/2)+1/2 ln(1/2)

simplify

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

- ln (2)

Decimal Notation

- 0.69314 \dots

Solution steps

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

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

Add similar elements:

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

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

Remove parentheses:

(a) = a

= ln (1) - ln (2)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (2)

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

= - ln (2)

4.57 + lo g_{10} (\frac{0.049}{0.21})

ln (\frac{54}{5.2})

\frac{5}{2} ln (5) + \frac{5}{2} ln (2)

\frac{ln ( 0.15 ) - ln ( 0.25 )}{- 6.7 \cdot 1 0 ^{- 4}}

3 lo g_{m} (z) - \frac{1}{5} lo g_{m} (w) + 6 lo g_{m} (x)

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