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

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

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

simplify

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

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

Solution steps

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

Group like terms

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

Factor out common term

lo g_{b} (x)

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

Simplify

lo g_{b} (x) (- 3 + \frac{1}{2}) : - lo g_{b} (x) \frac{5}{2}

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

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

lo g_{10} (a b^{3})

lo g_{2} (\frac{y}{8})

ln (\frac{3 x ^{2}}{( x + 1 ) ^{10}})

lo g_{10} (a^{5} b^{4})

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