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Popular >

simplify log_{169}(13)

Solution

simplify

lo g_{169} (13)

Solution

\frac{1}{2}

+1

Solution steps

lo g_{169} (13)

Factor the number:

169 = 1 3^{2}

= lo g_{1 3^{2}} (13)

Apply log rule:

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

lo g_{1 3^{2}} (13) = \frac{1}{2} lo g_{13} (13)

= \frac{1}{2} lo g_{13} (13)

Apply log rule:

lo g_{a} (a) = 1

lo g_{13} (13) = 1

= \frac{1}{2} \cdot 1

Multiply the numbers:

\frac{1}{2} \cdot 1 = \frac{1}{2}

= \frac{1}{2}

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Frequently Asked Questions (FAQ)

What is log_{169}(13) ?
The solution to log_{169}(13) is 1/2