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Popular >

simplify 3^{log_{9}(16)}

Solution

simplify

3^{l o g_{9} (16)}

Solution

4

Solution steps

3^{l o g_{9} (16)}

lo g_{9} (16) = 4 lo g_{9} (2)

= 3^{4 l o g_{9} (2)}

Factor the number:

9 = 3^{2}

= 3^{4 l o g_{3^{2}} (2)}

Apply log rule:

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

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

= 3^{4 \cdot \frac{1}{2} l o g_{3} (2)}

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

= 3^{2 l o g_{3} (2)}

Apply exponent rule:

a^{b c} = (a^{b})^{c}, a \geq 0

3^{2 l o g_{3} (2)} = (3^{l o g_{3} (2)})^{2}

= (3^{l o g_{3} (2)})^{2}

Apply log rule:

a^{l o g_{a} (b)} = b

3^{l o g_{3} (2)} = 2

= 2^{2}

2^{2} = 4

= 4

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Frequently Asked Questions (FAQ)

What is 3^{log_{9}(16)} ?
The solution to 3^{log_{9}(16)} is 4