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Popular >

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

Solution

simplify

3 ln (2) - 3 ln (3)

Solution

ln (\frac{8}{27})

+1

Decimal Notation

- 1.21639 \dots

Solution steps

3 ln (2) - 3 ln (3)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{2 ^{3}}{3 ^{3}} = \frac{8}{27}

= ln (\frac{8}{27})

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Frequently Asked Questions (FAQ)

What is 3ln(2)-3ln(3) ?
The solution to 3ln(2)-3ln(3) is ln(8/27)