Question 691401
2log(base9)x = 1/2 + log(base9)(5x + 18)
log(base9)x^2 = 1/2 + log(base9)(5x + 18)
log(base9)x^2 - log(base9)(5x + 18) = 1/2
log(base9)x^2/(5x + 18) = 1/2
x^2/(5x + 18) = 9^(1/2)
x^2/(5x + 18) = 3
x^2 = 3(5x + 18)
x^2 = 15x + 46
x^2-15X = 46
x^2-15X-46 = 0
Applying the "quadratic formula" yields:
x  = {17.61, -2.61}
throw out the negative solution (extraneous) leaving:
x = 17.61
.
details of quadratic follows:
*[invoke quadratic "x", 1, -15, -46 ]