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Popular >

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

Solution

simplify

3 ln (2) - 2 ln (3)

Solution

ln (\frac{8}{9})

+1

Decimal Notation

- 0.11778 \dots

Solution steps

3 ln (2) - 2 ln (3)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{2 ^{3}}{3 ^{2}} = \frac{8}{9}

= ln (\frac{8}{9})

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Frequently Asked Questions (FAQ)

What is 3ln(2)-2ln(3) ?
The solution to 3ln(2)-2ln(3) is ln(8/9)