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

The solution to log_{10}(x)-3log_{10}(3)-1/2 log_{10}(y) is log_{10}(x/(27sqrt(y)))

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

simplify

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

lo g_{10} (\frac{x}{27 y})

Solution steps

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

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

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

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (x) - lo g_{10} (3^{3}) = lo g_{10} (\frac{x}{3 ^{3}})

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

Simplify

\frac{\frac{x}{3 ^{3}}}{y ^{\frac{1}{2}}} : \frac{x}{27 y ^{\frac{1}{2}}}

= lo g_{10} (\frac{x}{27 y ^{\frac{1}{2}}})

Apply exponent rule:

a^{\frac{1}{2}} = a

y^{\frac{1}{2}} = y

= lo g_{10} (\frac{x}{27 y})

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What is log_{10}(x)-3log_{10}(3)-1/2 log_{10}(y) ?
The solution to log_{10}(x)-3log_{10}(3)-1/2 log_{10}(y) is log_{10}(x/(27sqrt(y)))