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

The solution to 1/4 log_{b}(x)+2log_{b}(y)-4log_{b}(x) is 2log_{b}(y)-15/4 log_{b}(x)

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

simplify

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

2 lo g_{b} (y) - \frac{15}{4} lo g_{b} (x)

Solution steps

\frac{1}{4} 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}{4} lo g_{b} (x)

Factor out common term

lo g_{b} (x)

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

Simplify

lo g_{b} (x) (- 4 + \frac{1}{4}) : - lo g_{b} (x) \frac{15}{4}

= 2 lo g_{b} (y) - lo g_{b} (x) \frac{15}{4}

= 2 lo g_{b} (y) - \frac{15}{4} lo g_{b} (x)

2 ln (x) - 5 ln (y)

lo g_{2} (\frac{x ^{5} 4 ^{x}}{2 ^{x^{4}}})

6 lo g_{10} (x) + 2 lo g_{10} (y)

lo g_{2} (x) - lo g_{2} (y) - 3 lo g_{2} (z)

What is 1/4 log_{b}(x)+2log_{b}(y)-4log_{b}(x) ?
The solution to 1/4 log_{b}(x)+2log_{b}(y)-4log_{b}(x) is 2log_{b}(y)-15/4 log_{b}(x)