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

The solution to (2ln(3)+ln(2))/(2ln(2)-ln(3)) is (ln(18))/(ln(4/3))

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

simplify

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

\frac{ln ( 18 )}{ln ( \frac{4}{3} )}

Decimal Notation

10.04710 \dots

Solution steps

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

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 ( 2 ) - ln ( 3 )}

Apply log rule:

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

ln (3^{2}) + ln (2) = ln (3^{2} \cdot 2)

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

3^{2} \cdot 2 = 18

= \frac{ln ( 18 )}{2 ln ( 2 ) - ln ( 3 )}

Apply log rule:

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

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

= \frac{ln ( 18 )}{ln ( 2 ^{2} ) - ln ( 3 )}

Apply log rule:

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

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

= \frac{ln ( 18 )}{ln ( \frac{2 ^{2}}{3} )}

2^{2} = 4

= \frac{ln ( 18 )}{ln ( \frac{4}{3} )}

ln (\frac{1}{2 \cdot π \cdot x})

lo g_{3} (10) - lo g_{3} (5) lo g_{3} (18)

lo g_{b} (2) + 2 lo g_{b} (x)

ln (3) (- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4}) + ln (2) (1 - \frac{1}{4} - \frac{3}{4})

ln (1) - ln (\frac{3}{2})

What is (2ln(3)+ln(2))/(2ln(2)-ln(3)) ?
The solution to (2ln(3)+ln(2))/(2ln(2)-ln(3)) is (ln(18))/(ln(4/3))