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

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

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simplify 1/3 log_{b}(x)+5log_{b}(y)-2log_{b}(x)

simplify

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

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

Solution steps

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

Group like terms

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

Factor out common term

lo g_{b} (x)

= 5 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}

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

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

ln (\frac{9 + 61}{10})

lo g_{10} (100 a)

ln (3) \frac{1}{7}

\frac{2}{3} lo g_{10} (27) + lo g_{10} (x) + lo g_{10} (x)

- (3 ln (2) + ln (3))

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