What is (ln(5)-ln(4))/(ln(3)-ln(2)) ?

The solution to (ln(5)-ln(4))/(ln(3)-ln(2)) is (ln(5/4))/(ln(3/2))

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simplify (ln(5)-ln(4))/(ln(3)-ln(2))

simplify

\frac{ln ( 5 ) - ln ( 4 )}{ln ( 3 ) - ln ( 2 )}

\frac{ln ( \frac{5}{4} )}{ln ( \frac{3}{2} )}

Decimal Notation

0.55033 \dots

Solution steps

\frac{ln ( 5 ) - ln ( 4 )}{ln ( 3 ) - ln ( 2 )}

Apply log rule:

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

ln (5) - ln (4) = ln (\frac{5}{4})

= \frac{ln ( \frac{5}{4} )}{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{5}{4} )}{ln ( \frac{3}{2} )}

lo g_{4} (\frac{1}{16} x)

ln (\frac{25}{7})

ln (\frac{8}{3 x ^{3} y})

lo g_{\frac{1}{2}} (\frac{7}{12})

3 ln (2) - \frac{1}{2} ln (4) + ln (5)

What is (ln(5)-ln(4))/(ln(3)-ln(2)) ?
The solution to (ln(5)-ln(4))/(ln(3)-ln(2)) is (ln(5/4))/(ln(3/2))