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

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

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

simplify

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

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

Decimal Notation

- 1

Solution steps

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

Apply log rule:

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

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

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

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

- lo g_{10} (2 x 1 0^{- 5})

2 (lo g_{7} (y) - 2 lo g_{7} (w)) + 3 lo g_{7} (z)

ln (\frac{10 π - 3 3}{6})

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

- lo g_{10} (5.4 \cdot 1 0^{- 5})

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