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The value of e^("log"(e) x+ "log"(sqr...

The value of
`e^("log"_(e) x+ "log"_(sqrt(e)) x+ "log"_(root(3)(e)) x + …. + "log"_(root(10)(e))x),` is

A

`x^(10)`

B

e

C

`x^(55)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`"log"_(e) x+ "log"_(sqrt(e)) x+ "log"_(root(3)(e)) x + …. + "log"_(root(10)(e))x`
` = (1+2+3+…+10)"log"_(e)x = "log"_(e)x = "log"_(e)x^(55)`
`therefore e^("log"_(e) x+ "log"_(sqrt(e)) x+ "log"_(root(3)(e)) x + …. + "log"_(root(10)(e))x) =e^("log"_(e)x^(55)) = x^(55)`
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