Math CentralQuandaries & Queries


Question from John, a student:


x= (y/z)ln((1+a^2)/(1-a^2))

Please solve for 'a'

Thanks in advance!

i John,

Multiply both sides by z/y to obtain

xz/y = ln[(1+a2)/(1-a2)]

Apply the exponential function t both sides so that the equation becomes

exz/y = eln[(1+a2)/(1-a2)] = (1+a2)/(1-a2)

Now solve for a.

I hope this helps,


John wrote back

Hi penny,

thanks for the answer with natural log.

I am still stuck with this question as I was stuck at the same point that you left off.

i.e. how to make 'a' subject of this equation?

e^(xz/y) = (1+a^2)/(1-a^2)

Thanks in advance!


Let me make the notation a little easier by writing k = exz/y then

k = (1+a2)/(1-a2)

Multiply each side by (1 - a2) and the equation becomes

(1 - a2) k = (1 + a2)

Simplify, solve for a and then substitute k = exz/y.


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