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Popular >

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

Solution

simplify

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

Solution

16

Solution steps

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

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

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

Factor the number:

9 = 3^{2}

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

Apply exponent rule:

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

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

Multiply the numbers:

2 \cdot 2 = 4

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

Apply exponent rule:

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

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

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

Apply log rule:

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

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

= 2^{4}

2^{4} = 16

= 16

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Frequently Asked Questions (FAQ)

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