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

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

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

simplify

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

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

Solution steps

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

Group like terms

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

Factor out common term

lo g_{b} (x)

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

Simplify

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

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

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

ln (\frac{2 x - 1}{x ^{3}})

2 ln (x) + x ln (3) - \frac{1}{2} ln (x + 1)

ln (\frac{4}{2})

lo g_{10} (\frac{x y}{z})

lo g_{2} (\frac{8}{x + 8})

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