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Popular >

simplify log_{8}(2)+log_{8}(4)

Solution

simplify

lo g_{8} (2) + lo g_{8} (4)

Solution

1

Solution steps

lo g_{8} (2) + lo g_{8} (4)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{8} (2) + lo g_{8} (4) = lo g_{8} (2 \cdot 4)

= lo g_{8} (2 \cdot 4)

Factor the number:

8 = 2^{3}

= lo g_{2^{3}} (2 \cdot 4)

Apply log rule:

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

lo g_{2^{3}} (2 \cdot 4) = \frac{1}{3} lo g_{2} (2 \cdot 4)

= \frac{1}{3} lo g_{2} (2 \cdot 4)

2 \cdot 4 = 2^{3}

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

Apply log rule:

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

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

= \frac{1}{3} \cdot 3

\frac{1}{3} \cdot 3 = 1

= 1

Popular Examples

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1420 (\frac{107}{143})^{7} + 70

x^{2} + 6 < 0

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x^{3} + x^{2} - 25 x - 25

factor 9x^8-30x^4+25 factor

9 x^{8} - 30 x^{4} + 25

2 p^{2} = - 4 p + 3

Frequently Asked Questions (FAQ)

What is log_{8}(2)+log_{8}(4) ?
The solution to log_{8}(2)+log_{8}(4) is 1