What is 1/3 log_{b}(x)+4log_{b}(y)-5log_{b}(x) ?

The solution to 1/3 log_{b}(x)+4log_{b}(y)-5log_{b}(x) is 4log_{b}(y)-14/3 log_{b}(x)

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simplify 1/3 log_{b}(x)+4log_{b}(y)-5log_{b}(x)

simplify

\frac{1}{3} lo g_{b} (x) + 4 lo g_{b} (y) - 5 lo g_{b} (x)

4 lo g_{b} (y) - \frac{14}{3} lo g_{b} (x)

Solution steps

\frac{1}{3} 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}{3} lo g_{b} (x)

Factor out common term

lo g_{b} (x)

= 4 lo g_{b} (y) + lo g_{b} (x) (- 5 + \frac{1}{3})

Simplify

lo g_{b} (x) (- 5 + \frac{1}{3}) : - lo g_{b} (x) \frac{14}{3}

= 4 lo g_{b} (y) - lo g_{b} (x) \frac{14}{3}

= 4 lo g_{b} (y) - \frac{14}{3} lo g_{b} (x)

lo g_{3} (x) - lo g_{3} (x^{5})

lo g_{10} (\frac{x}{10000})

- \frac{1}{2} ln ∣ x + 1 ∣ + \frac{1}{2} ln ∣ x - 1 ∣ + C

lo g_{5} (\frac{125}{x - 1})

ln (x (x - 3))

What is 1/3 log_{b}(x)+4log_{b}(y)-5log_{b}(x) ?
The solution to 1/3 log_{b}(x)+4log_{b}(y)-5log_{b}(x) is 4log_{b}(y)-14/3 log_{b}(x)