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

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

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simplify 1/2 log_{c}(x)+5log_{c}(y)-2log_{c}(x)

simplify

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

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

Solution steps

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

Group like terms

= 5 lo g_{c} (y) - 2 lo g_{c} (x) + \frac{1}{2} lo g_{c} (x)

Factor out common term

lo g_{c} (x)

= 5 lo g_{c} (y) + lo g_{c} (x) (- 2 + \frac{1}{2})

Simplify

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

= 5 lo g_{c} (y) - lo g_{c} (x) \frac{3}{2}

= 5 lo g_{c} (y) - \frac{3}{2} lo g_{c} (x)

lo g_{5} (x) - lo g_{5} (x^{2})

ln (22)

ln (x^{2} - 81) - ln (x + 9)

lo g_{10} (\frac{y ^{5} x}{z})

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