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Popular >

simplify 2log_{4}(9)

Solution

simplify

2 lo g_{4} (9)

Solution

2 lo g_{2} (3)

+1

Decimal Notation

3.16992 \dots

Solution steps

2 lo g_{4} (9)

Factor the number:

4 = 2^{2}

= 2 lo g_{2^{2}} (9)

Apply log rule:

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

lo g_{2^{2}} (9) = \frac{1}{2} lo g_{2} (9)

= 2 \cdot \frac{1}{2} lo g_{2} (9)

2 \cdot \frac{1}{2} lo g_{2} (9) = lo g_{2} (9)

= lo g_{2} (9)

Factor the number:

9 = 3^{2}

= lo g_{2} (3^{2})

Apply log rule:

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

lo g_{2} (3^{2}) = 2 lo g_{2} (3)

= 2 lo g_{2} (3)

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Frequently Asked Questions (FAQ)

What is 2log_{4}(9) ?
The solution to 2log_{4}(9) is 2log_{2}(3)