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Popular >

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

Solution

simplify

3 ln (3) - 2 ln (2)

Solution

ln (\frac{27}{4})

+1

Decimal Notation

1.90954 \dots

Solution steps

3 ln (3) - 2 ln (2)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{3 ^{3}}{2 ^{2}} = \frac{27}{4}

= ln (\frac{27}{4})

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Frequently Asked Questions (FAQ)

What is 3ln(3)-2ln(2) ?
The solution to 3ln(3)-2ln(2) is ln(27/4)