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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{2} ((2 x - 2)^{2}) - 4 lo g_{2} (1 - x)

- lo g_{10} (2.5 x \cdot 1 0^{- 7})

ln (96 x)

lo g_{5} (2 x)

ln (e x^{4})

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