Answer:
3/2 or 1/2
Step-by-step explanation:
Using the rules of logarithms, the expression can be rewritten as ...
... (8x -3)/4 = x^2
This is a regular quadratic that can be solved in any of the usual ways.
... x^2 -2x +3/4 = 0
... x^2 -2x +1 = 1 -3/4 . . . subtract 3/4, complete the square by adding 1
... (x -1)^2 = 1/4 . . . . . . . . simplify
... x -1 = ±1/2 . . . . . . . . . . take the square root
... x = 1 ± 1/2 . . . . . . . . . . add 1
... x = {3/2, 1/2}
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The attached graph shows the log equation and the quadratic have same solutions. (Each is put in the form f(x) = 0.) The x-intercepts represent the solutions.)
