What is 1/2 ln(a)+1/2 ln(b) ?

The solution to 1/2 ln(a)+1/2 ln(b) is ln(a^{1/2}b^{1/2})

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simplify 1/2 ln(a)+1/2 ln(b)

simplify

\frac{1}{2} ln (a) + \frac{1}{2} ln (b)

ln (a^{\frac{1}{2}} b^{\frac{1}{2}})

Solution steps

\frac{1}{2} ln (a) + \frac{1}{2} ln (b)

Apply log rule:

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

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

= ln (a^{\frac{1}{2}}) + \frac{1}{2} ln (b)

Apply log rule:

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

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

= ln (a^{\frac{1}{2}}) + ln (b^{\frac{1}{2}})

Apply log rule:

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

ln (a^{\frac{1}{2}}) + ln (b^{\frac{1}{2}}) = ln (a^{\frac{1}{2}} b^{\frac{1}{2}})

= ln (a^{\frac{1}{2}} b^{\frac{1}{2}})

ln (\frac{z + r ^{2} + z ^{2}}{- z + r ^{2} + z ^{2}})

6 ln (4 x)

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

lo g_{x} (\frac{a y ^{4}}{z ^{4}})

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