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Popular >

simplify log_{4}(169)

Solution

simplify

lo g_{4} (169)

Solution

lo g_{2} (13)

+1

Decimal Notation

3.70043 \dots

Solution steps

lo g_{4} (169)

Factor the number:

169 = 1 3^{2}

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

Apply log rule:

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

lo g_{4} (1 3^{2}) = 2 lo g_{4} (13)

= 2 lo g_{4} (13)

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

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

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

= lo g_{2} (13)

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Frequently Asked Questions (FAQ)

What is log_{4}(169) ?
The solution to log_{4}(169) is log_{2}(13)