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Popular >

simplify 25^{log_{5}(3)}

Solution

simplify

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

Solution

9

Solution steps

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

Factor the number:

25 = 5^{2}

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

Apply exponent rule:

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

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

Apply exponent rule:

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

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

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

Apply log rule:

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

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

= 3^{2}

3^{2} = 9

= 9

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Frequently Asked Questions (FAQ)

What is 25^{log_{5}(3)} ?
The solution to 25^{log_{5}(3)} is 9