What is log_{4}((x^2)/(yz)) ?

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

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simplify log_{4}((x^2)/(yz))

simplify

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

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

Solution steps

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

Apply log rule:

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

lo g_{4} (\frac{x ^{2}}{yz}) = lo g_{4} (x^{2}) - lo g_{4} (yz)

= lo g_{4} (x^{2}) - lo g_{4} (yz)

lo g_{4} (x^{2}) = lo g_{2} (x)

lo g_{4} (yz) = lo g_{4} (y) + lo g_{4} (z)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

ln (a \cdot b^{x})

ln (\frac{4}{1.213})

\frac{1}{2} lo g_{b} (x) + 3 lo g_{b} (y) - 5 lo g_{b} (x)

lo g_{5} (\frac{8}{x})

lo g_{10} (2 \cdot 7)

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