What is 1/2 log_{c}(x)+3log_{c}(y)-4log_{c}(x) ?

The solution to 1/2 log_{c}(x)+3log_{c}(y)-4log_{c}(x) is 3log_{c}(y)-7/2 log_{c}(x)

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simplify 1/2 log_{c}(x)+3log_{c}(y)-4log_{c}(x)

simplify

\frac{1}{2} lo g_{c} (x) + 3 lo g_{c} (y) - 4 lo g_{c} (x)

3 lo g_{c} (y) - \frac{7}{2} lo g_{c} (x)

Solution steps

\frac{1}{2} lo g_{c} (x) + 3 lo g_{c} (y) - 4 lo g_{c} (x)

Group like terms

= 3 lo g_{c} (y) - 4 lo g_{c} (x) + \frac{1}{2} lo g_{c} (x)

Factor out common term

lo g_{c} (x)

= 3 lo g_{c} (y) + lo g_{c} (x) (- 4 + \frac{1}{2})

Simplify

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

= 3 lo g_{c} (y) - lo g_{c} (x) \frac{7}{2}

= 3 lo g_{c} (y) - \frac{7}{2} lo g_{c} (x)

ln (y) - ln (3)

lo g_{10} (2) + lo g_{10} (6)

\frac{15}{4} ln (\frac{2}{5})

lo g_{10} (\frac{x ^{4}}{y})

What is 1/2 log_{c}(x)+3log_{c}(y)-4log_{c}(x) ?
The solution to 1/2 log_{c}(x)+3log_{c}(y)-4log_{c}(x) is 3log_{c}(y)-7/2 log_{c}(x)