First, let's review a couple of basics:
2 x log (something) is the same as log(something²)
The sum of the logs of 2 numbers is the same as the log of their product.
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So 2 log₄(x) = log₄(x²)
From the given equation: log₄(x²) + log₄(x-1) = 1
Sum of logs = log of the product: log₄( [x] [x-1] ) = 1
Raise 4 to the power of each side: (x) (x-1) = 4
Eliminate parentheses on the left: x² - x = 4
Subtract 4 from each side: x² - x - 4 = 0
Mash this through the quadratic formula, and you have
x = 0.5 + 0.5√17 = 2.562 (rounded)
x = 0.5 - 0.5√17 = -1.562 (rounded)
