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

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

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

simplify

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

- ln (2) + 3

Decimal Notation

2.30685 \dots

Solution steps

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

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

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

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

Group like terms

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

Add similar elements:

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

= - ln (2) + 4 - 1

Add/Subtract the numbers:

4 - 1 = 3

= - ln (2) + 3

lo g_{8} (\frac{( x - 4 ) ( x - 1 ) ( 3 )}{5 x})

ln (k y) - ln (k x)

ln (24) - 8 ln (2)

ln (x^{2} + 1) + ln (x^{2} + 3)

ln (8 u) + 38 u - 3

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