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

The solution to 1/2 log_{b}(x)+3log_{b}(y)-5log_{b}(x) is 3log_{b}(y)-9/2 log_{b}(x)

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simplify 1/2 log_{b}(x)+3log_{b}(y)-5log_{b}(x)

simplify

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

3 lo g_{b} (y) - \frac{9}{2} lo g_{b} (x)

Solution steps

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

Group like terms

= 3 lo g_{b} (y) - 5 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) (- 5 + \frac{1}{2})

Simplify

lo g_{b} (x) (- 5 + \frac{1}{2}) : - lo g_{b} (x) \frac{9}{2}

= 3 lo g_{b} (y) - lo g_{b} (x) \frac{9}{2}

= 3 lo g_{b} (y) - \frac{9}{2} lo g_{b} (x)

lo g_{5} (\frac{8}{x})

lo g_{10} (2 \cdot 7)

- lo g_{10} (3 \cdot 1 0^{- 4})

6 ln (x) - \frac{1}{6} ln (y)

ln (- 4 x)

What is 1/2 log_{b}(x)+3log_{b}(y)-5log_{b}(x) ?
The solution to 1/2 log_{b}(x)+3log_{b}(y)-5log_{b}(x) is 3log_{b}(y)-9/2 log_{b}(x)