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

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

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

simplify

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{2}{3} lo g_{2} (\frac{2}{3}) - \frac{1}{3} lo g_{2} (\frac{1}{3})

2 (lo g_{5} (x) + 2 lo g_{5} (y) - 3 lo g_{5} (z))

lo g_{b} (2 x)

lo g_{2} (A) + lo g_{2} (B) - 2 lo g_{2} (C)

ln (\frac{3}{5})

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