What is 1/2 ln(x)-1/2 ln(y) ?

The solution to 1/2 ln(x)-1/2 ln(y) is ln(sqrt(x/y))

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simplify 1/2 ln(x)-1/2 ln(y)

simplify

\frac{1}{2} ln (x) - \frac{1}{2} ln (y)

ln (\frac{x}{y})

Solution steps

\frac{1}{2} ln (x) - \frac{1}{2} ln (y)

Apply log rule:

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

\frac{1}{2} ln (x) = ln (x^{\frac{1}{2}})

= ln (x^{\frac{1}{2}}) - \frac{1}{2} ln (y)

Apply log rule:

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

\frac{1}{2} ln (y) = ln (y^{\frac{1}{2}})

= ln (x^{\frac{1}{2}}) - ln (y^{\frac{1}{2}})

Apply log rule:

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

ln (x^{\frac{1}{2}}) - ln (y^{\frac{1}{2}}) = ln (\frac{x ^{\frac{1}{2}}}{y ^{\frac{1}{2}}})

= ln (\frac{x ^{\frac{1}{2}}}{y ^{\frac{1}{2}}})

Combine same powers :

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

lo g_{10} (x) - lo g_{10} (5)

lo g_{10} (\frac{x ^{2} - 9}{x - 3})

ln (11 x) - (5 ln (x) + 4 ln (3 y))

ln (\frac{1.148}{2.87})

\frac{e ln ( 90 ) + ln ( 6 )}{ln ( 3 ) + ln ( 20 )}

What is 1/2 ln(x)-1/2 ln(y) ?
The solution to 1/2 ln(x)-1/2 ln(y) is ln(sqrt(x/y))