Solving a Logarithm?

Question

Solve the equation algebraically.
Round the result to three decimal places.

http://img48.imageshack.us/img48/4146/log4ur2.jpg

Answer 1

log 4 x - log 4 (x-1) = 1/2
log 4 [x(x-1)] = 1/2
log 4 (x^2 - x) = 1/2
4^(1/2) = x^2 - x
+/-2 = x^2 - x

solve for x
using +2
2 = x^2 - x
x^2 - x -2=0
(x-2)(x+1) = 0
x = 2
x = -1

using the -2 will result in a complex number.

therefore x = -1 or x = 2

that's it

Answer 2

x=2
(note log_4(x) means log base 4 of x)
********************
log_4(x) - log_4(x-1) = 1/2
log_4[x/(x-1)] = 1/2
4^(1/2) = x/(x-1)
2 = x/(x-1)
2(x-1) = x
2x - 2 = x
x = 2
no need to round anything