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

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

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

simplify

2 ln (2) - 2 ln (3)

ln (\frac{4}{9})

Decimal Notation

- 0.81093 \dots

Solution steps

2 ln (2) - 2 ln (3)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{2 ^{2}}{3 ^{2}} = \frac{4}{9}

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

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

2 lo g_{10} (0.000001) + 2 lo g_{10} (0.001)

ln (\frac{1.61}{3.792})

\frac{1}{2} lo g_{10} (z) - \frac{1}{4} lo g_{10} (y)

ln (x^{4} (1 - 2 x)^{2})