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Popular >

simplify 64^{log_{8}(sqrt(3))}

Solution

simplify

6 4^{l o g_{8} (3)}

Solution

3

Solution steps

6 4^{l o g_{8} (3)}

Factor the number:

64 = 2^{6}

= (2^{6})^{l o g_{8} (3)}

Apply exponent rule:

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

= 2^{6 l o g_{8} (3)}

6 lo g_{8} (3) = 3 lo g_{8} (3)

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

3 lo g_{8} (3) = lo g_{2} (3)

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

Apply log rule:

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

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

= 3

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Frequently Asked Questions (FAQ)

What is 64^{log_{8}(sqrt(3))} ?
The solution to 64^{log_{8}(sqrt(3))} is 3