Question

If f (x) = log (1+2x/1-2x)then x=
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Answer 1

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Answer 2

Therefore if f(x) = log [ (1+2x) / (1-2x) ] then the value of x is 2f(x).

Given:

f(x) = log [ (1+2x) / (1-2x) ]

To Find:

The value of 'x'.

Solution:

The given question can be solved as shown below.

Given function,

f(x) = log [ (1+2x) / (1-2x) ]

Let us find, f(2x/1+x²) means replace x by 2x / 1+x²

⇒ f (2x / 1+x² ) = log ( 1 + (2x) / (1+x²) )-log(1-(2x)/(1+x²))

⇒ {log(1+x²+2x)-log(1+x²)}-{log(1+x²–2x)-log(1+x²)}

⇒ log(1+x²+2x)-log(1+x²–2x)

⇒ log(x+1)²-log(x-1)²

⇒ 2{log(x+1)-log(x-1)}

⇒ 2{log((x+1)/(x-1))}

⇒ 2{f(x)}

Therefore if f(x) = log [ (1+2x) / (1-2x) ] then the value of x is 2f(x).

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