What is log_{4}(1/4 x^2y) ?

The solution to log_{4}(1/4 x^2y) is -1+log_{2}(x)+log_{4}(y)

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simplify log_{4}(1/4 x^2y)

simplify

lo g_{4} (\frac{1}{4} x^{2} y)

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

Solution steps

lo g_{4} (\frac{1}{4} x^{2} y)

\frac{1}{4} = 4^{- 1}

= lo g_{4} (4^{- 1} x^{2} y)

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{4} (4^{- 1} x^{2} y) = lo g_{4} (4^{- 1}) + lo g_{4} (x^{2} y)

= lo g_{4} (4^{- 1}) + lo g_{4} (x^{2} y)

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{4} (4^{- 1}) = - 1

= - 1 + lo g_{4} (x^{2} y)

Simplify

lo g_{4} (x^{2} y) : lo g_{2} (x) + lo g_{4} (y)

= - 1 + (lo g_{2} (x) + lo g_{4} (y))

Apply rule:

a + (b + c) = a + b + c

- 1 + (lo g_{2} (x) + lo g_{4} (y)) = - 1 + lo g_{2} (x) + lo g_{4} (y)

= - 1 + lo g_{2} (x) + lo g_{4} (y)

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

lo g_{10} (5) - lo g_{10} (3)

lo g_{10} (z) - lo g_{10} (12 x)

ln (x) - \frac{x}{θ} - 2 ln (θ)

- \frac{7}{12} lo g_{2} (\frac{7}{12}) - \frac{5}{12} lo g_{2} (\frac{5}{12})

What is log_{4}(1/4 x^2y) ?
The solution to log_{4}(1/4 x^2y) is -1+log_{2}(x)+log_{4}(y)