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

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

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

simplify

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

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

Decimal Notation

- 8.21439 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3^{2} = 9

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

lo g_{10} (\frac{x ^{2}}{y}) - 1

lo g_{2} (9 x y)

3 ln (y - x)

- \frac{3}{8} \cdot lo g_{2} (\frac{3}{8}) - \frac{5}{8} \cdot lo g_{2} (\frac{5}{8})

lo g_{7} (12 x) - lo g_{7} (7 x^{3})

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