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

The solution to 1/4 log_{c}(x)+4log_{c}(y)-3log_{c}(x) is 4log_{c}(y)-11/4 log_{c}(x)

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

simplify

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

4 lo g_{c} (y) - \frac{11}{4} lo g_{c} (x)

Solution steps

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

Group like terms

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

Factor out common term

lo g_{c} (x)

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

Simplify

lo g_{c} (x) (- 3 + \frac{1}{4}) : - lo g_{c} (x) \frac{11}{4}

= 4 lo g_{c} (y) - lo g_{c} (x) \frac{11}{4}

= 4 lo g_{c} (y) - \frac{11}{4} lo g_{c} (x)

- lo g_{10} (5 \cdot 1 0^{- 4})

ln (\frac{2}{4})

4 lo g_{7} (x) - 3 lo g_{7} (y)

- lo g_{10} (5 \cdot 1 0^{- 8})

ln ((x (4 y - 1)^{\frac{1}{3}})^{\frac{2}{5}})

What is 1/4 log_{c}(x)+4log_{c}(y)-3log_{c}(x) ?
The solution to 1/4 log_{c}(x)+4log_{c}(y)-3log_{c}(x) is 4log_{c}(y)-11/4 log_{c}(x)