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

The solution to 1/2 log_{a}(x)-2log_{a}(y) is log_{a}((x^{1/2})/(y^2))

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

2 lo g_{a} (y) = lo g_{a} (y^{2})

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

lo g_{10} (\frac{y}{x ^{4}})

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

\frac{1}{2} ln (\frac{c}{b ^{4} a})

ln (x + 1) - ln (x + 2)

lo g_{10} (x^{7})

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