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

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

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

simplify

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

\frac{2 ln ( 2 )}{ln ( \frac{4}{3} )}

Decimal Notation

4.81884 \dots

Solution steps

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

Apply log rule:

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

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

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

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})

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

2^{2} = 4

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

ln (500) - ln (200)

ln (5.5 \cdot 1 0^{(- 15)})

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

50 \cdot ln (\frac{72}{54.8})

- lo g_{10} (6.21 x 1 0^{- 5})

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