What is log_{1/4}(3sqrt(32)) ?

The solution to log_{1/4}(3sqrt(32)) is -log_{4}(3)-5/4

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simplify log_{1/4}(3sqrt(32))

simplify

lo g_{\frac{1}{4}} (332)

- lo g_{4} (3) - \frac{5}{4}

Solution steps

lo g_{\frac{1}{4}} (332)

Apply log rule:

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

lo g_{\frac{1}{4}} (332) = lo g_{\frac{1}{4}} (3) + lo g_{\frac{1}{4}} (32)

= lo g_{\frac{1}{4}} (3) + lo g_{\frac{1}{4}} (32)

lo g_{\frac{1}{4}} (32) = \frac{1}{2} lo g_{\frac{1}{4}} (32)

= lo g_{\frac{1}{4}} (3) + \frac{1}{2} lo g_{\frac{1}{4}} (32)

Apply log rule:

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

= - lo g_{4} (3) + \frac{1}{2} lo g_{\frac{1}{4}} (32)

\frac{1}{2} lo g_{\frac{1}{4}} (32) = - \frac{5}{4}

= - lo g_{4} (3) - \frac{5}{4}

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What is log_{1/4}(3sqrt(32)) ?
The solution to log_{1/4}(3sqrt(32)) is -log_{4}(3)-5/4