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

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

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

simplify

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

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

Solution steps

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

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

Apply log rule:

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

2 lo g_{10} (x) = lo g_{10} (x^{2})

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

lo g_{2} (\frac{x ^{3}}{y ^{6}})

lo g_{10} (\frac{y}{10000})

2 ln (x - 1) - \frac{1}{2} ln (y) - 3 ln (z)

\frac{2}{3} lo g_{a} (- 2 lo g_{b} (- \frac{1}{5} lo g_{c} (x)))

ln (2) - ln (10)

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