What is 1/2 log_{10}(x)+5log_{10}(y) ?

The solution to 1/2 log_{10}(x)+5log_{10}(y) is log_{10}(x^{1/2}y^5)

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simplify 1/2 log_{10}(x)+5log_{10}(y)

simplify

\frac{1}{2} lo g_{10} (x) + 5 lo g_{10} (y)

lo g_{10} (x^{\frac{1}{2}} y^{5})

Solution steps

\frac{1}{2} lo g_{10} (x) + 5 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}}) + 5 lo g_{10} (y)

Apply log rule:

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

5 lo g_{10} (y) = lo g_{10} (y^{5})

= lo g_{10} (x^{\frac{1}{2}}) + lo g_{10} (y^{5})

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^{5}) = lo g_{10} (y^{5} x^{\frac{1}{2}})

= lo g_{10} (x^{\frac{1}{2}} y^{5})

(lo g_{b} (x) - lo g_{b} (y)) + 7 lo g_{b} (v)

4 ln (x) + 3 ln (y) - 2 ln (z)

lo g_{2} (16 x^{3})

- ln (a) + ln (b)

What is 1/2 log_{10}(x)+5log_{10}(y) ?
The solution to 1/2 log_{10}(x)+5log_{10}(y) is log_{10}(x^{1/2}y^5)