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

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

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

simplify

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

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

Solution steps

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

Group like terms

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

Simplify

lo g_{c} (x) (- 2 + \frac{1}{3}) : - lo g_{c} (x) \frac{5}{3}

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

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

- lo g_{10} (5.2 \cdot 1 0^{- 8})

3 lo g_{5} (x - 1) - lo g_{5} (3 - 6 x)

ln (x) + ln (x - 4) - 2 ln (x + 1)

\frac{1}{2} (lo g_{10} (b) - lo g_{10} (c))

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