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Popular >

simplify log_{8}(16)-log_{8}(2)

Solution

simplify

lo g_{8} (16) - lo g_{8} (2)

Solution

1

Solution steps

lo g_{8} (16) - lo g_{8} (2)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{8} (16) - lo g_{8} (2) = lo g_{8} (\frac{16}{2})

= lo g_{8} (\frac{16}{2})

Factor the number:

8 = 2^{3}

= lo g_{2^{3}} (\frac{16}{2})

Apply log rule:

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

lo g_{2^{3}} (\frac{16}{2}) = \frac{1}{3} lo g_{2} (\frac{16}{2})

= \frac{1}{3} lo g_{2} (\frac{16}{2})

\frac{16}{2} = 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

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simplify 8/x-2/x simplify

\frac{8}{x} - \frac{2}{x}

\frac{7}{8} \div \frac{1}{2}

Frequently Asked Questions (FAQ)

What is log_{8}(16)-log_{8}(2) ?
The solution to log_{8}(16)-log_{8}(2) is 1