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

The solution to 1/2 log_{b}(x)+4log_{b}(y)-5log_{b}(x) is 4log_{b}(y)-9/2 log_{b}(x)

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

simplify

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

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

Solution steps

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

Group like terms

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

Factor out common term

lo g_{b} (x)

= 4 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}

= 4 lo g_{b} (y) - lo g_{b} (x) \frac{9}{2}

= 4 lo g_{b} (y) - \frac{9}{2} lo g_{b} (x)

lo g_{2} (16 (x^{2} - 49))

ln (\frac{2}{25})

lo g_{x^{5}} (2 x^{2})

lo g_{3} (9 x^{4})

ln (x^{2} - 3 x - 4) - ln (x - 4) + ln (x + 1)

What is 1/2 log_{b}(x)+4log_{b}(y)-5log_{b}(x) ?
The solution to 1/2 log_{b}(x)+4log_{b}(y)-5log_{b}(x) is 4log_{b}(y)-9/2 log_{b}(x)