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

The solution to 1/3 log_{c}(x)+3log_{c}(y)-5log_{c}(x) is 3log_{c}(y)-14/3 log_{c}(x)

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

simplify

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

3 lo g_{c} (y) - \frac{14}{3} lo g_{c} (x)

Solution steps

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

Factor out common term

lo g_{c} (x)

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

Simplify

lo g_{c} (x) (- 5 + \frac{1}{3}) : - lo g_{c} (x) \frac{14}{3}

= 3 lo g_{c} (y) - lo g_{c} (x) \frac{14}{3}

= 3 lo g_{c} (y) - \frac{14}{3} lo g_{c} (x)

ln (\frac{13}{3})

(3 lo g_{7} (m) + 12 lo g_{7} (n)) - 3 lo g_{7} (p)

lo g_{6} (c a \cdot b)

- ln (\frac{4}{5})

6 lo g_{9} (z) + 6 lo g_{9} (x) - 2 lo g_{9} (y)

What is 1/3 log_{c}(x)+3log_{c}(y)-5log_{c}(x) ?
The solution to 1/3 log_{c}(x)+3log_{c}(y)-5log_{c}(x) is 3log_{c}(y)-14/3 log_{c}(x)