SOLUTION: b = ( a^x + a^-x )/ 2 find x

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Question 325607: b = ( a^x + a^-x )/ 2 find x
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
b = ( a^x + a^-x )/ 2=cosh(xln(a))
=> x=acosh(b)/ln(a)
or 2ba^x=a^(2x)+1 => a^(2x)-2b*a^x+1=0
a^x=(2b+-sqrt(4b^2-4)/2=b+-sqrt(b^2-1)
x=ln(b+-sqrt(b^2-1))/ln(a)