Question

ch2p2.9q50

Plz explain in detail step by step.
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Answer 1

Answer:

A

Step-by-step explanation:

Use componendo dividend both side

(x+1)/(x-1) =(2e^n) /(2e^-n)

(x+1)/(x-1)= e^n*e^n =e^2n

Taking log both side,

Log (x+1)/(x-1) =2n

Find n

U get option A

Hope it helps u

Answer 2

Step-by-step explanation:

$Given:x=\frac{e^n + e^{-n}}{e^n - e^{-n}}$

$=>x=\frac{e^n + \frac{1}{e^n}}{e^n - \frac{1}{e^n}}$

$=> x= \frac{e^{2x}+1}{e^{2x}-1}$

$=>x * e^{2x} - x = e^{2x} + 1$

$=>1 + x = e^{2x} - x * e^{2x}$

$=>1 + x = e^{2x}(1 - x)$

$=>e^{2x} = \frac{1 + x}{1 - x}$

Apply  'log' on both sides, we get

$=>loge^{2x} = log\frac{1+x}{1-x}$

$=>2x log e = log\frac{1+x}{1-x}$

$=>2x = log\frac{1+x}{1-x}$

$=> \boxed{x = \frac{1}{2}log\frac{1+x}{1-x}}$

Hope it helps