What is 1/4 log_{b}(x)+4log_{b}(y)-5log_{b}(x) ?

The solution to 1/4 log_{b}(x)+4log_{b}(y)-5log_{b}(x) is 4log_{b}(y)-19/4 log_{b}(x)

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simplify 1/4 log_{b}(x)+4log_{b}(y)-5log_{b}(x)

simplify

\frac{1}{4} lo g_{b} (x) + 4 lo g_{b} (y) - 5 lo g_{b} (x)

4 lo g_{b} (y) - \frac{19}{4} lo g_{b} (x)

Solution steps

\frac{1}{4} lo g_{b} (x) + 4 lo g_{b} (y) - 5 lo g_{b} (x)

Group like terms

= 4 lo g_{b} (y) - 5 lo g_{b} (x) + \frac{1}{4} lo g_{b} (x)

Factor out common term

lo g_{b} (x)

= 4 lo g_{b} (y) + lo g_{b} (x) (- 5 + \frac{1}{4})

Simplify

lo g_{b} (x) (- 5 + \frac{1}{4}) : - lo g_{b} (x) \frac{19}{4}

= 4 lo g_{b} (y) - lo g_{b} (x) \frac{19}{4}

= 4 lo g_{b} (y) - \frac{19}{4} lo g_{b} (x)

5 \cdot lo g_{8} (c^{3} d^{2}) + 3 \cdot lo g_{8} (c d^{7})

2 lo g_{4} (y) + 5 lo g_{4} (x) - \frac{1}{2} lo g_{4} (z)

lo g_{10} (\frac{x ^{2}}{y})

ln (\frac{10}{9})

\frac{1}{2} lo g_{10} (c) + 4 lo g_{10} (d)

What is 1/4 log_{b}(x)+4log_{b}(y)-5log_{b}(x) ?
The solution to 1/4 log_{b}(x)+4log_{b}(y)-5log_{b}(x) is 4log_{b}(y)-19/4 log_{b}(x)