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

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

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

simplify

2 ln (3) - 3 ln (2)

ln (\frac{9}{8})

Decimal Notation

0.11778 \dots

Solution steps

2 ln (3) - 3 ln (2)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

lo g_{10} (x) + lo g_{10} (y) + 3 lo g_{10} (z)

lo g_{b} (\frac{1}{10}) + lo g_{b} (40)

lo g_{2} (\frac{8}{x + 5})

lo g_{10} (x (x^{2} + 8)^{- \frac{1}{2}})

4 lo g_{10} (2) + lo g_{10} (6) - lo g_{10} (3)