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Popular >

simplify 1/5 (2ln(2)-ln(3))

Solution

simplify

\frac{1}{5} (2 ln (2) - ln (3))

Solution

\frac{1}{5} ln (\frac{4}{3})

+1

Decimal Notation

0.05753 \dots

Solution steps

\frac{1}{5} (2 ln (2) - ln (3))

Apply log rule:

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

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

= \frac{1}{5} (ln (2^{2}) - ln (3))

Apply log rule:

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

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

= \frac{1}{5} ln (\frac{2 ^{2}}{3})

2^{2} = 4

= \frac{1}{5} ln (\frac{4}{3})

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Frequently Asked Questions (FAQ)

What is 1/5 (2ln(2)-ln(3)) ?
The solution to 1/5 (2ln(2)-ln(3)) is 1/5 ln(4/3)