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

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

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

simplify

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

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

Decimal Notation

- 0.46084 \dots

Solution steps

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

3^{2} = 9

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

lo g_{10} ((x + y)^{3}) - lo g_{10} (x + y)

lo g_{4} (x^{2} - 1) - 5 lo g_{4} (x + 1)

lo g_{3} (\frac{100}{27 x})

ln (\frac{4 e ^{6}}{7 y})

lo g_{7} (x) - lo g_{7} (x^{2})

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