Find the inverse of the following.....please show steps! Having trouble getting rid of log in the exponent portion......I know you switch f(x)=y for the x in the exponent but then I don\'t know how to get rid of the log in the exponent. \\(f(x)= 5^{log_{3}(4x^{2}+1)} -7\\) Solution let f(x) = y then y+7 = 5^(log(base 3)(4x^2+1)) log(base 5)(y+7) = (log(base 3)(4x^2+1) =>4x^2+1 = 3^(log(base 5)(y+7)) => x = sqrt{[3^(log(base 5)(y+7))-1]/4}.

1. Find the inverse of the following.....please show steps! Having trouble getting rid of log in the
exponent portion......I know you switch f(x)=y for the x in the exponent but then I don't know
how to get rid of the log in the exponent.
(f(x)= 5^{log_{3}(4x^{2}+1)} -7)
Solution
let f(x) = y
then y+7 = 5^(log(base 3)(4x^2+1))
log(base 5)(y+7) = (log(base 3)(4x^2+1)
=>4x^2+1 = 3^(log(base 5)(y+7))
=> x = sqrt{[3^(log(base 5)(y+7))-1]/4}