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Popular >

simplify 8^{log_{4}(5)}

Solution

simplify

8^{l o g_{4} (5)}

Solution

5^{3}

+1

Decimal Notation

11.18033 \dots

Solution steps

8^{l o g_{4} (5)}

Factor the number:

8 = 2^{3}

= (2^{3})^{l o g_{4} (5)}

Apply exponent rule:

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

= 2^{3 l o g_{4} (5)}

Factor the number:

4 = 2^{2}

= 2^{3 l o g_{2^{2}} (5)}

Apply log rule:

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

lo g_{2^{2}} (5) = \frac{1}{2} lo g_{2} (5)

= 2^{3 \cdot \frac{1}{2} l o g_{2} (5)}

3 \cdot \frac{1}{2} = \frac{3}{2}

= 2^{\frac{3}{2} l o g_{2} (5)}

Apply exponent rule:

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

2^{\frac{3}{2} l o g_{2} (5)} = (2^{l o g_{2} (5)})^{\frac{3}{2}}

= (2^{l o g_{2} (5)})^{\frac{3}{2}}

Apply log rule:

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

2^{l o g_{2} (5)} = 5

= 5^{\frac{3}{2}}

5^{\frac{3}{2}} = 5^{3}

= 5^{3}

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Frequently Asked Questions (FAQ)

What is 8^{log_{4}(5)} ?
The solution to 8^{log_{4}(5)} is sqrt(5^3)