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

The solution to simplify-ln(x)-1/2 ln(y) is -ln(xy^{1/2})

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

simplify

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

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

Solution steps

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

Rewrite

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

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

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

ln (\frac{1}{2 \cdot π \cdot x})

lo g_{3} (10) - lo g_{3} (5) lo g_{3} (18)

lo g_{b} (2) + 2 lo g_{b} (x)

ln (3) (- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4}) + ln (2) (1 - \frac{1}{4} - \frac{3}{4})

What is simplify-ln(x)-1/2 ln(y) ?
The solution to simplify-ln(x)-1/2 ln(y) is -ln(xy^{1/2})