What is 3log_{10}(x)+1/2 log_{10}(y) ?

The solution to 3log_{10}(x)+1/2 log_{10}(y) is log_{10}(x^3y^{1/2})

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simplify 3log_{10}(x)+1/2 log_{10}(y)

simplify

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

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

Solution steps

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

Apply log rule:

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

3 lo g_{10} (x) = lo g_{10} (x^{3})

= lo g_{10} (x^{3}) + \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^{3}) + 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^{3}) + lo g_{10} (y^{\frac{1}{2}}) = lo g_{10} (x^{3} y^{\frac{1}{2}})

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

ln (1) - ln (4 x) - ln (3 x - 5)

2 \cdot 1 0^{l o g_{2} (x) + l o g_{2} (x^{2})}

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

\frac{5}{2} ln (\frac{5}{2})

lo g_{10} (x y^{3})

What is 3log_{10}(x)+1/2 log_{10}(y) ?
The solution to 3log_{10}(x)+1/2 log_{10}(y) is log_{10}(x^3y^{1/2})