Solve exactly Enter your answers in terms of b and in increa

Solve exactly:

Enter your answers in terms of b and in increasing order.

Solution

3log_bx+3 log_b(1-x) = 6

3 log_b(x+3)(1-x)=6

log_b(x+3)(1-x)=2

x-x²+3-3x=b²

x²+2x-3=-b²

x²+2x=-b²+3

x²+2x+1 =-b²+3+1

(x+1)²=4-b²

x+1=+-sqrt(4-b²)

x=-1+-sqrt(4-b²)

log cant take negative values

So the answer is

x=-1 +sqrt(4-b²)