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Popular >

simplify log_{4}(x^2)

Solution

simplify

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

Solution

lo g_{2} (x)

Solution steps

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

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

= 2 lo g_{4} (x)

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

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

Simplify

2 \cdot \frac{1}{2} lo g_{2} (x) : lo g_{2} (x)

= lo g_{2} (x)

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Frequently Asked Questions (FAQ)

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