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

The solution to 1/3 log_{b}(x)+2log_{b}(y)-3log_{b}(x) is 2log_{b}(y)-8/3 log_{b}(x)

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

simplify

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

2 lo g_{b} (y) - \frac{8}{3} lo g_{b} (x)

Solution steps

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

Group like terms

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

Factor out common term

lo g_{b} (x)

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

Simplify

lo g_{b} (x) (- 3 + \frac{1}{3}) : - lo g_{b} (x) \frac{8}{3}

= 2 lo g_{b} (y) - lo g_{b} (x) \frac{8}{3}

= 2 lo g_{b} (y) - \frac{8}{3} lo g_{b} (x)

ln (\frac{( 2 y + 1 ) ^{5}}{y ^{2} + 1})

lo g_{10} (3) - lo g_{10} (4)

ln (\frac{( 1 + 5 )}{2})

4 lo g_{10} (x) + 7 lo g_{10} (y)

lo g_{5} (\frac{25}{x + 3})

What is 1/3 log_{b}(x)+2log_{b}(y)-3log_{b}(x) ?
The solution to 1/3 log_{b}(x)+2log_{b}(y)-3log_{b}(x) is 2log_{b}(y)-8/3 log_{b}(x)