What is 1/2 log_{10}(x)+log_{10}(y) ?

The solution to 1/2 log_{10}(x)+log_{10}(y) is log_{10}(x^{1/2}y)

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simplify 1/2 log_{10}(x)+log_{10}(y)

simplify

\frac{1}{2} lo g_{10} (x) + lo g_{10} (y)

lo g_{10} (x^{\frac{1}{2}} y)

Solution steps

\frac{1}{2} lo g_{10} (x) + lo g_{10} (y)

Apply log rule:

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

\frac{1}{2} lo g_{10} (x) = lo g_{10} (x^{\frac{1}{2}})

= lo g_{10} (x^{\frac{1}{2}}) + lo g_{10} (y)

Apply log rule:

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

lo g_{10} (x^{\frac{1}{2}}) + lo g_{10} (y) = lo g_{10} (y x^{\frac{1}{2}})

= lo g_{10} (x^{\frac{1}{2}} y)

0.33 \cdot lo g_{10} (0.33) + 0.67 \cdot lo g_{10} (0.67)

ln (x) + ln (x) + 3 ln (3 x)

lo g_{10} (\frac{2}{3})

ln (a - b) + ln (a + b)

ln v + v^{2} - ln ∣ v ∣

What is 1/2 log_{10}(x)+log_{10}(y) ?
The solution to 1/2 log_{10}(x)+log_{10}(y) is log_{10}(x^{1/2}y)