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

The solution to 1/3 log_{c}(x)+4log_{c}(y)-5log_{c}(x) is 4log_{c}(y)-14/3 log_{c}(x)

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simplify 1/3 log_{c}(x)+4log_{c}(y)-5log_{c}(x)

simplify

\frac{1}{3} lo g_{c} (x) + 4 lo g_{c} (y) - 5 lo g_{c} (x)

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

Solution steps

\frac{1}{3} lo g_{c} (x) + 4 lo g_{c} (y) - 5 lo g_{c} (x)

Group like terms

= 4 lo g_{c} (y) - 5 lo g_{c} (x) + \frac{1}{3} lo g_{c} (x)

Factor out common term

lo g_{c} (x)

= 4 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}

= 4 lo g_{c} (y) - lo g_{c} (x) \frac{14}{3}

= 4 lo g_{c} (y) - \frac{14}{3} lo g_{c} (x)

lo g_{3} (3 x)

ln (\frac{( e ^{x} )}{1 + e ^{x}})

lo g_{5} (6) + lo g_{5} (8) - lo g_{5} (12)

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

lo g_{10} (\frac{y ^{7}}{x z ^{3}})

What is 1/3 log_{c}(x)+4log_{c}(y)-5log_{c}(x) ?
The solution to 1/3 log_{c}(x)+4log_{c}(y)-5log_{c}(x) is 4log_{c}(y)-14/3 log_{c}(x)