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

The solution to (ln(3)-ln(2))/(ln(2)+ln(3)) is (ln(3/2))/(ln(6))

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

simplify

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

\frac{ln ( \frac{3}{2} )}{ln ( 6 )}

Decimal Notation

0.22629 \dots

Solution steps

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

Apply log rule:

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

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

= \frac{ln ( \frac{3}{2} )}{ln ( 2 ) + ln ( 3 )}

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (2) + ln (3) = ln (2 \cdot 3)

= \frac{ln ( \frac{3}{2} )}{ln ( 2 \cdot 3 )}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{ln ( \frac{3}{2} )}{ln ( 6 )}

ln (\frac{1 + y}{2})

- 1.2124 \cdot ln (\frac{0.1}{10})

lo g_{10} (\frac{( x ^{2} y ^{5} )}{z ^{3}})

3 ln (- \frac{1}{2} (ln (b) + ln (c^{2})))

\frac{- 10 \cdot ln ( \frac{80}{180} )}{ln ( \frac{55}{180} ) + ln ( \frac{80}{180} )}

What is (ln(3)-ln(2))/(ln(2)+ln(3)) ?
The solution to (ln(3)-ln(2))/(ln(2)+ln(3)) is (ln(3/2))/(ln(6))