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

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

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

simplify

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

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

Solution steps

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

Group like terms

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

Factor out common term

lo g_{b} (x)

= 3 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}

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

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

lo g_{8} (10) - lo g_{8} (2)

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

\frac{3}{2} ln x^{2} + x + \frac{1}{2} ln (8)

lo g_{3} (\frac{9}{x + 2})

lo g_{10} (2) 3

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