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

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

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

simplify

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

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

Solution steps

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

Group like terms

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

Factor out common term

lo g_{b} (x)

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

Simplify

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

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

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

1 - ln (\frac{2}{3})

lo g_{8} (\frac{3 x ^{3}}{( 4 ) ( 3 )})

lo g_{4} (x + 1) + lo g_{4} (x) - 4 lo g_{4} (4)

3 ln (x) + \frac{1}{2} ln (y) - 4 ln (z)

lo g_{10} (x + 2) + lo g_{10} (x - 1)

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