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

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

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

simplify

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

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

Solution steps

\frac{1}{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})

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

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

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

lo g_{10} (\frac{27 a}{b})

ln (\frac{x}{x - 4}) + ln (\frac{x + 4}{x}) - ln (x^{2} - 16)

3 lo g_{10} (x) + lo g_{10} (2)

ln (4 x^{2})

- lo g_{10} (x + 6) + lo g_{10} (x - 5)

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