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

The solution to (2ln(3)-ln(2))/(2ln(3)-3ln(2)) is (ln(9/2))/(ln(9/8))

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

simplify

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

\frac{ln ( \frac{9}{2} )}{ln ( \frac{9}{8} )}

Decimal Notation

12.76989 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3^{2} = 9

= \frac{ln ( \frac{9}{2} )}{2 ln ( 3 ) - 3 ln ( 2 )}

Apply log rule:

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

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

= \frac{ln ( \frac{9}{2} )}{ln ( 3 ^{2} ) - 3 ln ( 2 )}

Apply log rule:

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

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

= \frac{ln ( \frac{9}{2} )}{ln ( 3 ^{2} ) - ln ( 2 ^{3} )}

Apply log rule:

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

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

= \frac{ln ( \frac{9}{2} )}{ln ( \frac{3 ^{2}}{2 ^{3}} )}

\frac{3 ^{2}}{2 ^{3}} = \frac{9}{8}

= \frac{ln ( \frac{9}{2} )}{ln ( \frac{9}{8} )}

0.026 ln (\frac{0.702}{8 \cdot 1 0 ^{- 16}})

lo g_{3} (\frac{6 x ^{5}}{7 w ^{2} y ^{3}})

4 (lo g_{a} (x) - 5 lo g_{a} (y)) + 3 lo g_{a} (z)

- 3 ln ∣ x + 2 ∣ + x - ln ∣ x - 2 ∣

ln (\frac{e ^{x}}{sin ( x ) ( x - 2 ) ^{2}})

What is (2ln(3)-ln(2))/(2ln(3)-3ln(2)) ?
The solution to (2ln(3)-ln(2))/(2ln(3)-3ln(2)) is (ln(9/2))/(ln(9/8))