Precalculus, Chapter 3, 3.4, Section 3.4, Problem 62

Given
log(8x) - log(1 + sqrt(x)) = 2 ---------------------(1)
On simplification we get
=> As we know log(a) - log(b) = log(a/b)
so ,
=> log(8x) - log(1 + sqrt(x)) = 2
=> log((8x)/(1 + sqrt(x))) = 2
=> log((8x)/(1 + sqrt(x))) = log 10^2 [as 2= log_10 (10^2) ]
=> removing log on both sides we get
=>(8x)/(1 + sqrt(x)) = 10 ^2
=>8x = 100(1+sqrt(x))
=>(8x - 100 ) = 100 sqrt(x)
=> squaring on both sides we get
=> (8x-100)^2 = 10000x
=>64x^2 +10000 -1600x = 10000x
=>64x^2 +10000 - 11600x = 0
=>on simplification we get
x= +- (25/8)(29+5sqrt(33))

on verification by substituting the values of x in the equation (1)
we get x= + (25/8)(29+5sqrt(33))
as cannot be solved x= - (25/8)(29+5sqrt(33)) when "sqrt(x)"
so,
x= (25/8)(29+5sqrt(33))
=> x = 180.384