What is log^2_{0.25}(\sqrt[3]{2}) ?

The solution to log^2_{0.25}(\sqrt[3]{2}) is 0.02777…

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simplify log^2_{0.25}(\sqrt[3]{2})

simplify

0.02777 \dots

Solution steps

Simplify

= (\frac{1}{3} lo g_{0.25} (2))^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= (\frac{1}{3})^{2} lo g_{0.25} (2)^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{1}{3})^{2} = \frac{1 ^{2}}{3 ^{2}}

= \frac{1 ^{2}}{3 ^{2}} lo g_{0.25} (2)^{2}

Apply rule

1^{a} = 1

1^{2} = 1

= \frac{1}{3 ^{2}} lo g_{0.25} (2)^{2}

\frac{1}{3 ^{2}} = 0.11111 \dots

= 0.11111 \dots lo g_{0.25} (2)^{2}

lo g_{0.25} (2)^{2} = 0.25

= 0.11111 \dots \cdot 0.25

Multiply the numbers:

0.11111 \dots \cdot 0.25 = 0.02777 \dots

= 0.02777 \dots

(a + 3) (a - 3)

- 2.5 (4 x - 3)

- 6 \div 2

10 \div 5

5 \div \frac{1}{2}

What is log^2_{0.25}(\sqrt[3]{2}) ?
The solution to log^2_{0.25}(\sqrt[3]{2}) is 0.02777…