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

The solution to 1/2 log_{c}(x)+3log_{c}(y)-5log_{c}(x) is 3log_{c}(y)-9/2 log_{c}(x)

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simplify 1/2 log_{c}(x)+3log_{c}(y)-5log_{c}(x)

simplify

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

3 lo g_{c} (y) - \frac{9}{2} lo g_{c} (x)

Solution steps

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

Group like terms

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

Factor out common term

lo g_{c} (x)

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

Simplify

lo g_{c} (x) (- 5 + \frac{1}{2}) : - lo g_{c} (x) \frac{9}{2}

= 3 lo g_{c} (y) - lo g_{c} (x) \frac{9}{2}

= 3 lo g_{c} (y) - \frac{9}{2} lo g_{c} (x)

- 2 - lo g_{4} (z) - lo g_{4} (x^{3} - 27)

lo g_{10} (- 3 i)

lo g_{10} (x y^{9})

lo g_{4} (20) + lo g_{4} (5)

lo g_{10} (\frac{365}{2.4}) + 2.8

What is 1/2 log_{c}(x)+3log_{c}(y)-5log_{c}(x) ?
The solution to 1/2 log_{c}(x)+3log_{c}(y)-5log_{c}(x) is 3log_{c}(y)-9/2 log_{c}(x)