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

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

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

simplify

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

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

Solution steps

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

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

Apply exponent rule:

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

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

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

ln (\frac{81}{125})

ln (x) - 2 ln (y)

lo g_{10} (\frac{a ^{6}}{b ^{5} c})

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

lo g_{3} (4 x^{2} y) + lo g_{3} (5 x^{3} y^{2})

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