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

The solution to 1/2 log_{b}(x)+2log_{b}(y)-4log_{b}(x) is 2log_{b}(y)-7/2 log_{b}(x)

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

simplify

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

2 lo g_{b} (y) - \frac{7}{2} lo g_{b} (x)

Solution steps

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

Group like terms

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

Factor out common term

lo g_{b} (x)

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

Simplify

lo g_{b} (x) (- 4 + \frac{1}{2}) : - lo g_{b} (x) \frac{7}{2}

= 2 lo g_{b} (y) - lo g_{b} (x) \frac{7}{2}

= 2 lo g_{b} (y) - \frac{7}{2} lo g_{b} (x)

lo g_{3} (\frac{27 x ^{3} y ^{2} - 1}{y ( x - 1 ) ^{2}})

ln (2 (1))

7 lo g_{5} (p) - lo g_{5} (q)

\frac{1}{2} ln (\frac{x + 1}{x - 1}) + e^{s i n (x^{2})} + ln (3)

What is 1/2 log_{b}(x)+2log_{b}(y)-4log_{b}(x) ?
The solution to 1/2 log_{b}(x)+2log_{b}(y)-4log_{b}(x) is 2log_{b}(y)-7/2 log_{b}(x)