How do you simplify [tex]5^{\log_5 x}[/tex]?

Question

Anonymous · Answer

5 l o g 5 ​ x = x ; D : x ∈ R + 5 l o g 5 ​ x = a l o g 5 ​ 5 l o g 5 ​ x = l o g 5 ​ a l o g 5 ​ x ⋅ l o g 5 ​ 5 = l o g 5 ​ a l o g 5 ​ x = l o g 5 ​ a ⟺ x = a ⇒ 5 l o g 5 ​ x = x

Anonymous · Answer

The expression 5 l o g 5 ​ x simplifies directly to x due to the inverse relationship between logarithms and exponentials. This simplification holds true for positive values of x . 
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How do you simplify [tex]5^{\log_5 x}[/tex]?

Answer (2)

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