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If #n=(a^x-a^(-x))/(a^x+a^(-x))# then find #log_a((1+n)/(1-n))#. Ans=2n

1 Answer
Dean R.
Jul 10, 2018

#n=(a^x-a^(-x))/(a^x+a^(-x))#

#1 + n = (a^x+a^(-x) + a^x-a^(-x))/(a^x+a^(-x)) = (2a^x)/(a^x+a^(-x))#

#1 - n = (a^x+a^(-x) - a^x + a^(-x))/(a^x+a^(-x)) = (2a^(-x))/(a^x+a^(-x))#

#(1+n)/(1-n) = (2a^x)/ (2a^(-x))=a^{2x}#

#log_a((1+n)/(1-n)) = 2 x#

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