What is 1/2 log_{c}(x)+4log_{c}(y)-3log_{c}(x) ?

The solution to 1/2 log_{c}(x)+4log_{c}(y)-3log_{c}(x) is 4log_{c}(y)-5/2 log_{c}(x)

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simplify 1/2 log_{c}(x)+4log_{c}(y)-3log_{c}(x)

simplify

\frac{1}{2} lo g_{c} (x) + 4 lo g_{c} (y) - 3 lo g_{c} (x)

4 lo g_{c} (y) - \frac{5}{2} lo g_{c} (x)

Solution steps

\frac{1}{2} lo g_{c} (x) + 4 lo g_{c} (y) - 3 lo g_{c} (x)

Group like terms

= 4 lo g_{c} (y) - 3 lo g_{c} (x) + \frac{1}{2} lo g_{c} (x)

Factor out common term

lo g_{c} (x)

= 4 lo g_{c} (y) + lo g_{c} (x) (- 3 + \frac{1}{2})

Simplify

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

= 4 lo g_{c} (y) - lo g_{c} (x) \frac{5}{2}

= 4 lo g_{c} (y) - \frac{5}{2} lo g_{c} (x)

ln (12 x)

lo g_{b} (9) + 3 lo g_{b} (2)

\frac{1}{4} lo g_{c} (x) + 3 lo g_{c} (y) - 2 lo g_{c} (x)

ln (x e^{- x})

lo g_{2} (7) + 3 lo g_{2} (x) - lo g_{2} (y)

What is 1/2 log_{c}(x)+4log_{c}(y)-3log_{c}(x) ?
The solution to 1/2 log_{c}(x)+4log_{c}(y)-3log_{c}(x) is 4log_{c}(y)-5/2 log_{c}(x)