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Popular >

simplify log_{4}(log_{3}(9))

Solution

simplify

lo g_{4} (lo g_{3} (9))

Solution

\frac{1}{2}

+1

Solution steps

lo g_{4} (lo g_{3} (9))

Factor the number:

4 = 2^{2}

= lo g_{2^{2}} (lo g_{3} (9))

Apply log rule:

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

lo g_{2^{2}} (lo g_{3} (9)) = \frac{1}{2} lo g_{2} (lo g_{3} (9))

= \frac{1}{2} lo g_{2} (lo g_{3} (9))

lo g_{3} (9) = 2

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 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_{4}(log_{3}(9)) ?
The solution to log_{4}(log_{3}(9)) is 1/2