What is log_{4}((sqrt(y))/(5z^2)) ?

The solution to log_{4}((sqrt(y))/(5z^2)) is log_{4}(sqrt(y))-log_{4}(5)-log_{2}(z)

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simplify log_{4}((sqrt(y))/(5z^2))

simplify

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

lo g_{4} (y) - lo g_{4} (5) - lo g_{2} (z)

Solution steps

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

Apply log rule:

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

lo g_{4} (\frac{y}{5 z ^{2}}) = lo g_{4} (y) - lo g_{4} (5 z^{2})

= lo g_{4} (y) - lo g_{4} (5 z^{2})

Simplify

lo g_{4} (5 z^{2}) : lo g_{4} (5) + lo g_{2} (z)

= lo g_{4} (y) - (lo g_{4} (5) + lo g_{2} (z))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{4} (5) + lo g_{2} (z)) = - lo g_{4} (5) - lo g_{2} (z)

= lo g_{4} (y) - lo g_{4} (5) - lo g_{2} (z)

- ln (y) - ln (x)

\frac{1}{3} ln (x + 8) + \frac{1}{2} ln (x - 1)

lo g_{a} (x) + lo g_{a} (y) - lo g_{a} (f)

\frac{1}{4} lo g_{b} (x) + 5 lo g_{b} (y) - 3 lo g_{b} (x)

What is log_{4}((sqrt(y))/(5z^2)) ?
The solution to log_{4}((sqrt(y))/(5z^2)) is log_{4}(sqrt(y))-log_{4}(5)-log_{2}(z)