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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

2 lo g_{10} (x) = lo g_{10} (x^{2})

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

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

ln (7) - 2 ln (2)

4 ln (\frac{16}{21})

lo g_{3} (\frac{3}{2}) + lo g_{3} (4.5)

\frac{1}{2} lo g_{10} (x) - lo g_{10} (3 y)

ln (\frac{9310}{3045})

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