What is 2ln(3)-ln(4)-ln(2) ?

The solution to 2ln(3)-ln(4)-ln(2) is ln(9/8)

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simplify 2ln(3)-ln(4)-ln(2)

simplify

2 ln (3) - ln (4) - ln (2)

ln (\frac{9}{8})

Decimal

0.11778 \dots

Solution steps

2 ln (3) - ln (4) - ln (2)

Apply log rule:

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

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

= ln (3^{2}) - ln (4) - ln (2)

Apply log rule:

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

ln (3^{2}) - ln (4) = ln (\frac{3 ^{2}}{4})

= ln (\frac{3 ^{2}}{4}) - ln (2)

3^{2} = 9

= ln (\frac{9}{4}) - ln (2)

Apply log rule:

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

ln (\frac{9}{4}) - ln (2) = ln (\frac{\frac{9}{4}}{2})

= ln (\frac{\frac{9}{4}}{2})

\frac{\frac{9}{4}}{2} = \frac{9}{8}

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

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