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

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

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

simplify

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

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

Decimal Notation

- 5.88494 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

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

ln (\frac{1}{1} - 0.1) + 9 ln (\frac{269}{9})

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

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

5.23 + lo g_{10} (\frac{1.76 \cdot 1 0 ^{- 3}}{0.00322})

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