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

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

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

simplify

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

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

Solution steps

\frac{1}{2} 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}{2} lo g_{c} (x)

Factor out common term

lo g_{c} (x)

= 4 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}

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

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

ln (a b^{2})

lo g_{10} (x) + 3 lo g_{10} (y) - 4 lo g_{10} (z)

ln (z (z - 1)^{2})

ln (\frac{6.05 + 8.05}{31.8})

lo g_{9} (5) + lo g_{9} (7)

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