What is 1/2 log_{a}(x)+4log_{a}(y)-2log_{a}(x) ?

The solution to 1/2 log_{a}(x)+4log_{a}(y)-2log_{a}(x) is 4log_{a}(y)-3/2 log_{a}(x)

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simplify 1/2 log_{a}(x)+4log_{a}(y)-2log_{a}(x)

simplify

\frac{1}{2} lo g_{a} (x) + 4 lo g_{a} (y) - 2 lo g_{a} (x)

4 lo g_{a} (y) - \frac{3}{2} lo g_{a} (x)

Solution steps

\frac{1}{2} lo g_{a} (x) + 4 lo g_{a} (y) - 2 lo g_{a} (x)

Group like terms

= 4 lo g_{a} (y) - 2 lo g_{a} (x) + \frac{1}{2} lo g_{a} (x)

Factor out common term

lo g_{a} (x)

= 4 lo g_{a} (y) + lo g_{a} (x) (- 2 + \frac{1}{2})

Simplify

lo g_{a} (x) (- 2 + \frac{1}{2}) : - lo g_{a} (x) \frac{3}{2}

= 4 lo g_{a} (y) - lo g_{a} (x) \frac{3}{2}

= 4 lo g_{a} (y) - \frac{3}{2} lo g_{a} (x)

ln (\frac{1}{x})

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

lo g_{5} (x y)

ln (\frac{x}{6})

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

What is 1/2 log_{a}(x)+4log_{a}(y)-2log_{a}(x) ?
The solution to 1/2 log_{a}(x)+4log_{a}(y)-2log_{a}(x) is 4log_{a}(y)-3/2 log_{a}(x)