What is 0.5log_{10}(x)+0.5log_{10}(y) ?

The solution to 0.5log_{10}(x)+0.5log_{10}(y) is log_{10}(x^{0.5}y^{0.5})

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simplify 0.5log_{10}(x)+0.5log_{10}(y)

simplify

0.5 lo g_{10} (x) + 0.5 lo g_{10} (y)

lo g_{10} (x^{0.5} y^{0.5})

Solution steps

0.5 lo g_{10} (x) + 0.5 lo g_{10} (y)

Apply log rule:

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

0.5 lo g_{10} (x) = lo g_{10} (x^{0.5})

= lo g_{10} (x^{0.5}) + 0.5 lo g_{10} (y)

Apply log rule:

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

0.5 lo g_{10} (y) = lo g_{10} (y^{0.5})

= lo g_{10} (x^{0.5}) + lo g_{10} (y^{0.5})

Apply log rule:

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

lo g_{10} (x^{0.5}) + lo g_{10} (y^{0.5}) = lo g_{10} (x^{0.5} y^{0.5})

= lo g_{10} (x^{0.5} y^{0.5})

lo g_{a} (\frac{1}{25})

- lo g_{10} (2.87 \cdot 1 0^{- 6})

ln (\frac{2 ^{4}}{3 ^{2} 5 ^{3}})

lo g_{2} (13 x + 14) - lo g_{2} (\frac{1}{13 x - 14})

ln (8 z)

What is 0.5log_{10}(x)+0.5log_{10}(y) ?
The solution to 0.5log_{10}(x)+0.5log_{10}(y) is log_{10}(x^{0.5}y^{0.5})