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Popular >

simplify 16^{log_{4}(7)}

Solution

simplify

1 6^{l o g_{4} (7)}

Solution

49

Solution steps

1 6^{l o g_{4} (7)}

Factor the number:

16 = 2^{4}

= (2^{4})^{l o g_{4} (7)}

Apply exponent rule:

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

= 2^{4 l o g_{4} (7)}

Factor the number:

4 = 2^{2}

= 2^{4 l o g_{2^{2}} (7)}

Apply log rule:

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

lo g_{2^{2}} (7) = \frac{1}{2} lo g_{2} (7)

= 2^{4 \cdot \frac{1}{2} l o g_{2} (7)}

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

= 2^{2 l o g_{2} (7)}

Apply exponent rule:

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

2^{2 l o g_{2} (7)} = (2^{l o g_{2} (7)})^{2}

= (2^{l o g_{2} (7)})^{2}

Apply log rule:

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

2^{l o g_{2} (7)} = 7

= 7^{2}

7^{2} = 49

= 49

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Frequently Asked Questions (FAQ)

What is 16^{log_{4}(7)} ?
The solution to 16^{log_{4}(7)} is 49