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

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

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

simplify

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

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

Solution steps

\frac{1}{4} 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}{4} lo g_{b} (x)

Factor out common term

lo g_{b} (x)

= 4 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}

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

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

lo g_{b} (\frac{a}{y})

ln (\frac{x}{x + 1})

lo g_{2} (x) + lo g_{2} (10) - 5 lo g_{2} (x)

lo g_{b} (24) - lo g_{b} (8)

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