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

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

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

simplify

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

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

Solution steps

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

Group like terms

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

Factor out common term

lo g_{c} (x)

= 2 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}

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

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

- lo g_{10} (1.9 \cdot 1 0^{- 6})

lo g_{3} (x^{2} - 25) - lo g_{3} (x - 5)

lo g_{5} (\frac{c}{25})

x y + ln (\frac{x}{e})

- lo g_{10} (2.643 \cdot 1 0^{- 7})

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