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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

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

3 lo g_{7} (2) + 2 lo g_{7} (3)

lo g_{8} (x - 6) + lo g_{8} (x + 6)

lo g_{10} (\frac{9 x}{y})

ln (9 + s^{2}) - ln (25 + s^{2})

lo g_{10} (4 a^{5} b^{4})

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