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Popular >

simplify log_{4}(49)

Solution

simplify

lo g_{4} (49)

Solution

lo g_{2} (7)

+1

Solution steps

lo g_{4} (49)

Factor the number:

49 = 7^{2}

= lo g_{4} (7^{2})

Apply log rule:

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

lo g_{4} (7^{2}) = 2 lo g_{4} (7)

= 2 lo g_{4} (7)

Factor the number:

4 = 2^{2}

= 2 lo g_{2^{2}} (7)

Apply log rule:

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

lo g_{2^{2}} (7) = \frac{1}{2} lo g_{2} (7)

= 2 \cdot \frac{1}{2} lo g_{2} (7)

2 \cdot \frac{1}{2} lo g_{2} (7) = lo g_{2} (7)

= lo g_{2} (7)

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\frac{3}{4} x - \frac{1}{2} = 1

Frequently Asked Questions (FAQ)

What is log_{4}(49) ?
The solution to log_{4}(49) is log_{2}(7)