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Let x and a be positive real numbers S...

Let x and a be positive real numbers
Statement 1: The sum of theries
`1+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+(log_(e)x)^(2)+…to infty is x`
Statement2: The sum of the series
`1+(xlog_(e)a)+(x^(2))/(2!)(log_(e)x))^(2)+(x^(3))/(3!)(log_(e)a)^(3)/(3!)+to infty is a^(x)`

A

1

B

2

C

3

D

statement 1 is true and statement 2 is a correct explantion for statement-1

Text Solution

Verified by Experts

We have
`1+(x log_(e)a)+(x^(2))/(2!)(log_(e)a)^()+(x^(3))/(3!)(log_(e)a)^(3)+ to infty`
`=e^(xlog_(e) a)=e^(log_(e)a^(x)=a^(x)`
So statement 2 is true
Replacing x by 1 and a by x in statemnt 2 we obtain statement 1 so statement 1 is true and statement 2 is a correct explantion for statement-1
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