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

The solution to 1/3 log_{c}(x)+2log_{c}(y)-3log_{c}(x) is 2log_{c}(y)-8/3 log_{c}(x)

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

simplify

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

2 lo g_{c} (y) - \frac{8}{3} lo g_{c} (x)

Solution steps

\frac{1}{3} 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}{3} lo g_{c} (x)

Factor out common term

lo g_{c} (x)

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

Simplify

lo g_{c} (x) (- 3 + \frac{1}{3}) : - lo g_{c} (x) \frac{8}{3}

= 2 lo g_{c} (y) - lo g_{c} (x) \frac{8}{3}

= 2 lo g_{c} (y) - \frac{8}{3} lo g_{c} (x)

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

ln (x^{2} cos (x))

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

lo g_{b} (\frac{16}{25})

What is 1/3 log_{c}(x)+2log_{c}(y)-3log_{c}(x) ?
The solution to 1/3 log_{c}(x)+2log_{c}(y)-3log_{c}(x) is 2log_{c}(y)-8/3 log_{c}(x)