What is (3ln(2)-3ln(3))/(ln(24)) ?

The solution to (3ln(2)-3ln(3))/(ln(24)) is (ln(8/27))/(ln(24))

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simplify (3ln(2)-3ln(3))/(ln(24))

simplify

\frac{3 ln ( 2 ) - 3 ln ( 3 )}{ln ( 24 )}

\frac{ln ( \frac{8}{27} )}{ln ( 24 )}

Decimal Notation

- 0.38274 \dots

Solution steps

\frac{3 ln ( 2 ) - 3 ln ( 3 )}{ln ( 24 )}

Apply log rule:

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

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

= \frac{ln ( 2 ^{3} ) - 3 ln ( 3 )}{ln ( 24 )}

Apply log rule:

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

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

= \frac{ln ( 2 ^{3} ) - ln ( 3 ^{3} )}{ln ( 24 )}

Apply log rule:

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

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

= \frac{ln ( \frac{2 ^{3}}{3 ^{3}} )}{ln ( 24 )}

\frac{2 ^{3}}{3 ^{3}} = \frac{8}{27}

= \frac{ln ( \frac{8}{27} )}{ln ( 24 )}

5 lo g_{b} (x) + 8 lo g_{b} (z)

ln (3 (1))

ln (\frac{e ^{7}}{5})

lo g_{w} (\frac{13 x}{2})

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

What is (3ln(2)-3ln(3))/(ln(24)) ?
The solution to (3ln(2)-3ln(3))/(ln(24)) is (ln(8/27))/(ln(24))