What is 1/4 log_{c}(x)+4log_{c}(y)-2log_{c}(x) ?

The solution to 1/4 log_{c}(x)+4log_{c}(y)-2log_{c}(x) is 4log_{c}(y)-7/4 log_{c}(x)

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simplify 1/4 log_{c}(x)+4log_{c}(y)-2log_{c}(x)

simplify

\frac{1}{4} lo g_{c} (x) + 4 lo g_{c} (y) - 2 lo g_{c} (x)

4 lo g_{c} (y) - \frac{7}{4} lo g_{c} (x)

Solution steps

\frac{1}{4} lo g_{c} (x) + 4 lo g_{c} (y) - 2 lo g_{c} (x)

Group like terms

= 4 lo g_{c} (y) - 2 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) (- 2 + \frac{1}{4})

Simplify

lo g_{c} (x) (- 2 + \frac{1}{4}) : - lo g_{c} (x) \frac{7}{4}

= 4 lo g_{c} (y) - lo g_{c} (x) \frac{7}{4}

= 4 lo g_{c} (y) - \frac{7}{4} lo g_{c} (x)

\frac{1}{3} lo g_{10} (x) - 4 lo g_{10} (y)

lo g_{4} (16 x^{8})

ln (\frac{1}{12})

ln (\frac{x ^{2} + 1}{x ^{2} - 1})

\frac{1}{3} lo g_{2} (3) + \frac{2}{3} lo g_{2} (\frac{3}{2})

What is 1/4 log_{c}(x)+4log_{c}(y)-2log_{c}(x) ?
The solution to 1/4 log_{c}(x)+4log_{c}(y)-2log_{c}(x) is 4log_{c}(y)-7/4 log_{c}(x)