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Popular >

simplify 3log_{8}(512)

Solution

simplify

3 lo g_{8} (512)

Solution

9

Solution steps

3 lo g_{8} (512)

Factor the number:

8 = 2^{3}

= 3 lo g_{2^{3}} (512)

Apply log rule:

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

lo g_{2^{3}} (512) = \frac{1}{3} lo g_{2} (512)

= 3 \cdot \frac{1}{3} lo g_{2} (512)

3 \cdot \frac{1}{3} lo g_{2} (512) = lo g_{2} (512)

= lo g_{2} (512)

Factor the number:

512 = 2^{9}

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

Apply log rule:

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

= 9

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Frequently Asked Questions (FAQ)

What is 3log_{8}(512) ?
The solution to 3log_{8}(512) is 9