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Popular >

simplify 4log_{4}(2)

Solution

simplify

4 lo g_{4} (2)

Solution

2

Solution steps

4 lo g_{4} (2)

Factor the number:

4 = 2^{2}

= 4 lo g_{2^{2}} (2)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

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

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= 4 \cdot \frac{1}{2} \cdot 1

Multiply the numbers:

\frac{1}{2} \cdot 1 = \frac{1}{2}

= 4 \cdot \frac{1}{2}

4 \cdot \frac{1}{2} = 2

= 2

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Frequently Asked Questions (FAQ)

What is 4log_{4}(2) ?
The solution to 4log_{4}(2) is 2