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Popular >

simplify log_{8}(27)

Solution

simplify

lo g_{8} (27)

Solution

lo g_{2} (3)

+1

Decimal Notation

1.58496 \dots

Solution steps

lo g_{8} (27)

Factor the number:

27 = 3^{3}

= lo g_{8} (3^{3})

Apply log rule:

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

lo g_{8} (3^{3}) = 3 lo g_{8} (3)

= 3 lo g_{8} (3)

Factor the number:

8 = 2^{3}

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

Apply log rule:

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

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

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

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

= lo g_{2} (3)

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Frequently Asked Questions (FAQ)

What is log_{8}(27) ?
The solution to log_{8}(27) is log_{2}(3)