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Popular >

simplify 25^{log_{5}(8)}

Solution

simplify

2 5^{l o g_{5} (8)}

Solution

64

Solution steps

2 5^{l o g_{5} (8)}

lo g_{5} (8) = 3 lo g_{5} (2)

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

Factor the number:

25 = 5^{2}

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

Apply exponent rule:

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

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

Multiply the numbers:

2 \cdot 3 = 6

= 5^{6 l o g_{5} (2)}

Apply exponent rule:

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

5^{6 l o g_{5} (2)} = (5^{l o g_{5} (2)})^{6}

= (5^{l o g_{5} (2)})^{6}

Apply log rule:

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

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

= 2^{6}

2^{6} = 64

= 64

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Frequently Asked Questions (FAQ)

What is 25^{log_{5}(8)} ?
The solution to 25^{log_{5}(8)} is 64