What is log_{b}((y^4)/(x^3sqrt(x^2))) ?

The solution to log_{b}((y^4)/(x^3sqrt(x^2))) is 4log_{b}(y)-4log_{b}(x)

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simplify log_{b}((y^4)/(x^3sqrt(x^2)))

simplify

lo g_{b} (\frac{y ^{4}}{x ^{3} x ^{2}})

4 lo g_{b} (y) - 4 lo g_{b} (x)

Solution steps

lo g_{b} (\frac{y ^{4}}{x ^{3} x ^{2}})

Simplify

x^{3} x^{2} : x^{4}

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

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

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

= lo g_{b} (y^{4}) - lo g_{b} (x^{4})

lo g_{b} (y^{4}) = 4 lo g_{b} (y)

lo g_{b} (x^{4}) = 4 lo g_{b} (x)

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

ln (\frac{x ^{8} p ^{5} q}{e ^{2}})

lo g_{\frac{1}{2}} (\frac{5}{2})

lo g_{10} (x - 1) - lo g_{10} (x - 2) - lo g_{10} (5)

- \frac{1}{8} lo g_{2} (\frac{1}{8}) - \frac{7}{8} lo g_{2} (\frac{7}{8})

2 lo g_{10} (m) + 3 lo g_{10} (n)

What is log_{b}((y^4)/(x^3sqrt(x^2))) ?
The solution to log_{b}((y^4)/(x^3sqrt(x^2))) is 4log_{b}(y)-4log_{b}(x)