What is (ln(1/3))/(ln(6)-ln(3)) ?

The solution to (ln(1/3))/(ln(6)-ln(3)) is -(ln(3))/(ln(2))

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simplify (ln(1/3))/(ln(6)-ln(3))

simplify

\frac{ln ( \frac{1}{3} )}{ln ( 6 ) - ln ( 3 )}

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

Decimal

- 1.58496 \dots

Solution steps

\frac{ln ( \frac{1}{3} )}{ln ( 6 ) - ln ( 3 )}

Apply log rule:

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

ln (6) - ln (3) = ln (\frac{6}{3})

= \frac{ln ( \frac{1}{3} )}{ln ( \frac{6}{3} )}

Divide the numbers:

\frac{6}{3} = 2

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

Simplify

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

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

lo g_{10} (3) lo g_{10} (2) + 2 lo g_{10} (3)

ln (\frac{T - 20}{200})

9 ln (x + 3) - 5 ln (x)

ln (\frac{x}{x + 1}) + \frac{1}{x + 1} + c

ln (\frac{x + a}{x - a})

What is (ln(1/3))/(ln(6)-ln(3)) ?
The solution to (ln(1/3))/(ln(6)-ln(3)) is -(ln(3))/(ln(2))