Question 552900
log(8x)-log(1+sqrtx)=2
log[8x/(1+√x)]=2
convert to exponential form
10^2=8x/(1+√x)=100
8x=100+100x^1/2
2x=25+25x^1/2
2x-25x^1/2-25=0
let u=x^1/2
u^2=x
2x^2-25u-25=0
By quadratic formula:
u=-0.930703=x^1/2 (reject, x^1/2>0)
or
u≈13.4307=x^1/2
x=u^2≈180.3837.. (ans)