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

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

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

simplify

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

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

Decimal Notation

1.70951 \dots

Solution steps

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

\frac{1}{2} lo g_{2} (127)

- lo g_{10} (3.1 \cdot 1 0^{- 5})

lo g_{5} (\frac{5}{7}) + lo g_{5} (\frac{49}{25})

lo g_{4} (\frac{7}{19}) + lo g_{4} (\frac{19}{7})

7 lo g_{6} (x - 2) + 2 lo g_{6} (3 x)

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