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

The solution to 1/2 ln(x)+1/2 ln(y) is ln(x^{1/2}y^{1/2})

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

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} (ab)

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

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

lo g_{10} (14) + \frac{1}{2} lo g_{10} (3) - lo g_{10} (2)

lo g_{5} (a^{2} + 10 a + 9) - lo g_{5} (a + 9) + 2

lo g_{10} (7.2) - lo g_{10} (6.7)

ln (12) - ln (5)

2 ln (5 y) + \frac{1}{x}

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