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

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

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

simplify

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

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

Decimal Notation

- 0.92169 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3^{2} = 9

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

- \frac{1}{ln ( 10 ) 0.5 \cdot lo g _{10} ( 0. 5 ^{2} )} - \frac{7}{( 0 , 5 + 3 ) ^{3}}

lo g_{3} (\frac{m}{n})

lo g_{b} (ab)

lo g_{10} (\frac{x ^{5}}{z ^{3} y ^{2}})

\frac{1}{4} lo g_{2} (4) + \frac{3}{4} lo g_{2} (\frac{4}{3})

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