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Popular >

simplify-4ln(2)-(-4)ln(6)

Solution

simplify

- 4 ln (2) - (- 4) ln (6)

Solution

4 ln (3)

+1

Decimal Notation

4.39444 \dots

Solution steps

- 4 ln (2) - (- 4) ln (6)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 ln (2) = ln (2^{4})

= - ln (2^{4}) - (- 4) ln (6)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

(- 4) ln (6) = ln (6^{(- 4)})

= - ln (2^{4}) - ln (6^{(- 4)})

Rewrite

- ln (2^{4}) - ln (6^{(- 4)})

as

- (ln (2^{4}) + ln (6^{(- 4)}))

= - (ln (2^{4}) + ln (6^{(- 4)}))

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (2^{4}) + ln (6^{(- 4)}) = ln (6^{- 4} \cdot 2^{4})

= - ln (6^{- 4} \cdot 2^{4})

2^{4} \cdot 6^{(- 4)} = \frac{1}{81}

= - ln (\frac{1}{81})

Simplify

ln (\frac{1}{81}) : - 4 ln (3)

= - (- 4 ln (3))

Apply rule

- (- a) = a

= 4 ln (3)

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Frequently Asked Questions (FAQ)

What is simplify-4ln(2)-(-4)ln(6) ?
The solution to simplify-4ln(2)-(-4)ln(6) is 4ln(3)