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

The solution to 1/3 log_{c}(x)+5log_{c}(y)-3log_{c}(x) is 5log_{c}(y)-8/3 log_{c}(x)

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

simplify

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

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

Solution steps

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

Group like terms

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

Factor out common term

lo g_{c} (x)

= 5 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}

= 5 lo g_{c} (y) - lo g_{c} (x) \frac{8}{3}

= 5 lo g_{c} (y) - \frac{8}{3} lo g_{c} (x)

lo g_{10} (x + 1) + lo g_{10} (x - 1)

2 lo g_{10} (12) - 3 lo g_{10} (6) + 2 lo g_{10} (2)

lo g_{7} ((\frac{x ^{5}}{y})^{5})

ln (x ln (x))

lo g_{10} (7) - lo g_{10} (x)

What is 1/3 log_{c}(x)+5log_{c}(y)-3log_{c}(x) ?
The solution to 1/3 log_{c}(x)+5log_{c}(y)-3log_{c}(x) is 5log_{c}(y)-8/3 log_{c}(x)