What is simplify-ln(3)+1/3+2ln(2) ?

The solution to simplify-ln(3)+1/3+2ln(2) is ln(4/3)+1/3

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

simplify

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

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

Solution steps

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

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})

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

2^{2} = 4

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

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