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Popular >

simplify 4ln(3)-2ln(2)

Solution

simplify

4 ln (3) - 2 ln (2)

Solution

ln (\frac{81}{4})

+1

Decimal Notation

3.00815 \dots

Solution steps

4 ln (3) - 2 ln (2)

Apply log rule:

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

4 ln (3) = ln (3^{4})

= ln (3^{4}) - 2 ln (2)

Apply log rule:

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

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

= ln (3^{4}) - ln (2^{2})

Apply log rule:

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

ln (3^{4}) - ln (2^{2}) = ln (\frac{3 ^{4}}{2 ^{2}})

= ln (\frac{3 ^{4}}{2 ^{2}})

\frac{3 ^{4}}{2 ^{2}} = \frac{81}{4}

= ln (\frac{81}{4})

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Frequently Asked Questions (FAQ)

What is 4ln(3)-2ln(2) ?
The solution to 4ln(3)-2ln(2) is ln(81/4)