What is (ln(4))/(ln(4)-2ln(3)) ?

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

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simplify (ln(4))/(ln(4)-2ln(3))

simplify

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

\frac{2 ln ( 2 )}{ln ( \frac{4}{9} )}

Decimal

- 1.70951 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3^{2} = 9

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

Simplify

ln (4) : 2 ln (2)

= \frac{2 ln ( 2 )}{ln ( \frac{4}{9} )}

3 lo g_{5} (a) + 4 lo g_{5} (b)

2 ln (4) + 2 ln (3)

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

ln (x^{2} + 3 x) - ln (x^{2} + x)

ln (8) - 2 ln (4) + ln (15)

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