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Popular >

simplify 8^{log_{2}(3)}

Solution

simplify

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

Solution

27

Solution steps

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

Factor the number:

8 = 2^{3}

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

Apply exponent rule:

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

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

Apply exponent rule:

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

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

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

Apply log rule:

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

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

= 3^{3}

3^{3} = 27

= 27

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Frequently Asked Questions (FAQ)

What is 8^{log_{2}(3)} ?
The solution to 8^{log_{2}(3)} is 27