What is log_{1/9}((\sqrt[3]{81})^2) ?

The solution to log_{1/9}((\sqrt[3]{81})^2) is -4/3

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simplify log_{1/9}((\sqrt[3]{81})^2)

simplify

- \frac{4}{3}

Decimal Notation

- 1.33333 \dots

Solution steps

Apply log rule:

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

= - lo g_{9} (9^{\frac{4}{3}})

Apply log rule:

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

lo g_{9} (9^{\frac{4}{3}}) = \frac{4}{3}

= - \frac{4}{3}

lo g_{2} (52)

3 cos^{2} (3 x) + 3 sin^{2} (3 x)

cos^{2} (x) (sec^{2} (x) - 1)

cos^{2} (x) - cos (x)

ln (e^{x y})

What is log_{1/9}((\sqrt[3]{81})^2) ?
The solution to log_{1/9}((\sqrt[3]{81})^2) is -4/3