Question 325607
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)