What is expand log_{1/4}(16z(x^3-27)) ?

The solution to expand log_{1/4}(16z(x^3-27)) is -2-log_{4}(z)-log_{4}(x^3-27)

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expand log_{1/4}(16z(x^3-27))

expand

lo g_{\frac{1}{4}} (16 z (x^{3} - 27))

- 2 - lo g_{4} (z) - lo g_{4} (x^{3} - 27)

Solution steps

lo g_{\frac{1}{4}} (16 z (x^{3} - 27))

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{\frac{1}{4}} (16 z (x^{3} - 27)) = lo g_{\frac{1}{4}} (16) + lo g_{\frac{1}{4}} (z) + lo g_{\frac{1}{4}} (x^{3} - 27)

= lo g_{\frac{1}{4}} (16) + lo g_{\frac{1}{4}} (z) + lo g_{\frac{1}{4}} (x^{3} - 27)

lo g_{\frac{1}{4}} (16) = - 2

= - 2 + lo g_{\frac{1}{4}} (z) + lo g_{\frac{1}{4}} (x^{3} - 27)

Apply log rule:

lo g_{\frac{1}{a}} (x) = - lo g_{a} (x)

= - 2 - lo g_{4} (z) + lo g_{\frac{1}{4}} (x^{3} - 27)

Apply log rule:

lo g_{\frac{1}{a}} (x) = - lo g_{a} (x)

= - 2 - lo g_{4} (z) - lo g_{4} (x^{3} - 27)

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

lo g_{z} (\frac{2 x}{3})

- lo g_{10} (3 \cdot 1 0^{- 3})

ln (2) - 3 ln (3)

What is expand log_{1/4}(16z(x^3-27)) ?
The solution to expand log_{1/4}(16z(x^3-27)) is -2-log_{4}(z)-log_{4}(x^3-27)