What is 1/3 log_{b}(x)+4log_{b}(y)-2log_{b}(x) ?

The solution to 1/3 log_{b}(x)+4log_{b}(y)-2log_{b}(x) is 4log_{b}(y)-5/3 log_{b}(x)

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simplify 1/3 log_{b}(x)+4log_{b}(y)-2log_{b}(x)

simplify

\frac{1}{3} lo g_{b} (x) + 4 lo g_{b} (y) - 2 lo g_{b} (x)

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

Solution steps

\frac{1}{3} lo g_{b} (x) + 4 lo g_{b} (y) - 2 lo g_{b} (x)

Group like terms

= 4 lo g_{b} (y) - 2 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) (- 2 + \frac{1}{3})

Simplify

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

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

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

2 lo g_{10} (2) + 3 lo g_{10} (3) - 2 lo g_{10} (6)

lo g_{10} (\frac{a ^{5} a ^{2} b}{( ab ) ^{2}})

lo g_{10} (y^{5} x)

lo g_{a} (\frac{y ^{5} w ^{2}}{x ^{4} z ^{3}})

ln (3 arccos (x))

What is 1/3 log_{b}(x)+4log_{b}(y)-2log_{b}(x) ?
The solution to 1/3 log_{b}(x)+4log_{b}(y)-2log_{b}(x) is 4log_{b}(y)-5/3 log_{b}(x)