What is simplify-(3ln(2/3))/(ln(9/4)-ln(2/3)) ?

The solution to simplify-(3ln(2/3))/(ln(9/4)-ln(2/3)) is -(3ln(2/3))/(ln(27/8))

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simplify-(3ln(2/3))/(ln(9/4)-ln(2/3))

simplify

- \frac{3 ln ( \frac{2}{3} )}{ln ( \frac{9}{4} ) - ln ( \frac{2}{3} )}

- \frac{3 ln ( \frac{2}{3} )}{ln ( \frac{27}{8} )}

Decimal Notation

1

Solution steps

- \frac{3 ln ( \frac{2}{3} )}{ln ( \frac{9}{4} ) - ln ( \frac{2}{3} )}

Apply log rule:

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

ln (\frac{9}{4}) - ln (\frac{2}{3}) = ln (\frac{\frac{9}{4}}{\frac{2}{3}})

= - \frac{3 ln ( \frac{2}{3} )}{ln ( \frac{\frac{9}{4}}{\frac{2}{3}} )}

\frac{\frac{9}{4}}{\frac{2}{3}} = \frac{27}{8}

= - \frac{3 ln ( \frac{2}{3} )}{ln ( \frac{27}{8} )}

\frac{- ln ( \frac{7}{2} ) + 2 ln ( 10 )}{ln ( 10 )}

ln (x e^{- x})

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

7 lo g_{5} (x) + 12 lo g_{5} (y)

3 lo g_{10} (x + 5) - lo g_{10} (x - 2)

What is simplify-(3ln(2/3))/(ln(9/4)-ln(2/3)) ?
The solution to simplify-(3ln(2/3))/(ln(9/4)-ln(2/3)) is -(3ln(2/3))/(ln(27/8))