What is (ln(x))/(ln(y)-ln(x)) ?

The solution to (ln(x))/(ln(y)-ln(x)) is (ln(x))/(ln(y/x))

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simplify (ln(x))/(ln(y)-ln(x))

simplify

\frac{ln ( x )}{ln ( y ) - ln ( x )}

\frac{ln ( x )}{ln ( \frac{y}{x} )}

Solution steps

\frac{ln ( x )}{ln ( y ) - ln ( x )}

Apply log rule:

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

ln (y) - ln (x) = ln (\frac{y}{x})

= \frac{ln ( x )}{ln ( \frac{y}{x} )}

- ln (\frac{0.5}{ln ( 2 )})

ln (\frac{9}{6})

- lo g_{10} (2.49 \cdot 1 0^{- 7})

lo g_{e} (8000) - lo g_{e} (4000)

ln (y) + ln (c)

What is (ln(x))/(ln(y)-ln(x)) ?
The solution to (ln(x))/(ln(y)-ln(x)) is (ln(x))/(ln(y/x))