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

The solution to 1/2 log_{a}(x)+3log_{a}(y)-3log_{a}(x) is 3log_{a}(y)-5/2 log_{a}(x)

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

simplify

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

3 lo g_{a} (y) - \frac{5}{2} lo g_{a} (x)

Solution steps

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

Group like terms

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

Factor out common term

lo g_{a} (x)

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

Simplify

lo g_{a} (x) (- 3 + \frac{1}{2}) : - lo g_{a} (x) \frac{5}{2}

= 3 lo g_{a} (y) - lo g_{a} (x) \frac{5}{2}

= 3 lo g_{a} (y) - \frac{5}{2} lo g_{a} (x)

ln (12) - ln (3)

lo g_{10} (\frac{10 a \cdot 0.1}{10})

lo g_{4} (\frac{64}{x + 3})

ln (\frac{x ^{2}}{4 x + 1})

lo g_{10} (16 x^{2}) + 2 lo g_{10} (\frac{1}{x})

What is 1/2 log_{a}(x)+3log_{a}(y)-3log_{a}(x) ?
The solution to 1/2 log_{a}(x)+3log_{a}(y)-3log_{a}(x) is 3log_{a}(y)-5/2 log_{a}(x)