What is (9ln(5))/(2ln(3)-ln(5)) ?

The solution to (9ln(5))/(2ln(3)-ln(5)) is (9ln(5))/(ln(9/5))

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simplify (9ln(5))/(2ln(3)-ln(5))

simplify

\frac{9 ln ( 5 )}{2 ln ( 3 ) - ln ( 5 )}

\frac{9 ln ( 5 )}{ln ( \frac{9}{5} )}

Decimal Notation

24.64319 \dots

Solution steps

\frac{9 ln ( 5 )}{2 ln ( 3 ) - ln ( 5 )}

Apply log rule:

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

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

= \frac{9 ln ( 5 )}{ln ( 3 ^{2} ) - ln ( 5 )}

Apply log rule:

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

ln (3^{2}) - ln (5) = ln (\frac{3 ^{2}}{5})

= \frac{9 ln ( 5 )}{ln ( \frac{3 ^{2}}{5} )}

3^{2} = 9

= \frac{9 ln ( 5 )}{ln ( \frac{9}{5} )}

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

lo g_{10} (a) + 4 lo g_{10} (b)

- (\frac{3}{7}) lo g_{2} (\frac{3}{7}) - (\frac{4}{7}) lo g_{2} (\frac{4}{7})

2 ln (2) - ln (5)

ln (\frac{0.6}{0.4})

What is (9ln(5))/(2ln(3)-ln(5)) ?
The solution to (9ln(5))/(2ln(3)-ln(5)) is (9ln(5))/(ln(9/5))