What is 1/4 log_{b}(x)+5log_{b}(y)-2log_{b}(x) ?

The solution to 1/4 log_{b}(x)+5log_{b}(y)-2log_{b}(x) is 5log_{b}(y)-7/4 log_{b}(x)

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simplify 1/4 log_{b}(x)+5log_{b}(y)-2log_{b}(x)

simplify

\frac{1}{4} lo g_{b} (x) + 5 lo g_{b} (y) - 2 lo g_{b} (x)

5 lo g_{b} (y) - \frac{7}{4} lo g_{b} (x)

Solution steps

\frac{1}{4} lo g_{b} (x) + 5 lo g_{b} (y) - 2 lo g_{b} (x)

Group like terms

= 5 lo g_{b} (y) - 2 lo g_{b} (x) + \frac{1}{4} lo g_{b} (x)

Factor out common term

lo g_{b} (x)

= 5 lo g_{b} (y) + lo g_{b} (x) (- 2 + \frac{1}{4})

Simplify

lo g_{b} (x) (- 2 + \frac{1}{4}) : - lo g_{b} (x) \frac{7}{4}

= 5 lo g_{b} (y) - lo g_{b} (x) \frac{7}{4}

= 5 lo g_{b} (y) - \frac{7}{4} lo g_{b} (x)

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lo g_{5} (8 x) - lo g_{5} (5 x + 7)

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What is 1/4 log_{b}(x)+5log_{b}(y)-2log_{b}(x) ?
The solution to 1/4 log_{b}(x)+5log_{b}(y)-2log_{b}(x) is 5log_{b}(y)-7/4 log_{b}(x)