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

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

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

simplify

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

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

Decimal Notation

3.81884 \dots

Solution steps

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

2^{2} = 4

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

lo g_{4} (\frac{1}{4} x^{2})

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

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

3 lo g_{e} (x) - 4 lo g_{e} (y)

lo g_{2} (\frac{16}{y})

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