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

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

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

simplify

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

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

Decimal Notation

0.18260 \dots

Solution steps

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

Apply log rule:

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

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

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

3^{2} = 9

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

\frac{ln ( 7 ) - ln ( 10 )}{5.37}

- ln (1.5 \cdot 1 0^{- 3})

lo g_{10} (- 4 i)

0.065 \cdot ln (\frac{5}{150})

ln (3.9) - ln (2.91)

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