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Popular >

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

Solution

simplify

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

Solution

12 ln (2)

+1

Decimal Notation

8.31776 \dots

Solution steps

4 ln (4) - 4 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 ln (4) - 4 (ln (1) - ln (2))

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

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

Apply rule

- (- a) = a

= 4 ln (4) + 4 ln (2)

4 ln (4) = 8 ln (2)

= 8 ln (2) + 4 ln (2)

Add similar elements:

8 ln (2) + 4 ln (2) = 12 ln (2)

= 12 ln (2)

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Frequently Asked Questions (FAQ)

What is 4ln(4)-4ln(1/2) ?
The solution to 4ln(4)-4ln(1/2) is 12ln(2)