list the potential solutions to 2log x - log3 = log3 from least to greatest. x = or x =

Explanation:

Step1: Use logarithm property

Using the property (n\log a=\log(a^{n})), rewrite (2\log x) as (\log(x^{2})). The equation (2\log x-\log3 = \log3) becomes (\log(x^{2})-\log3=\log3).

Step2: Use subtraction - logarithm property

Using the property (\log a-\log b=\log\frac{a}{b}), we have (\log\frac{x^{2}}{3}=\log3).

Step3: Remove logarithms

Since the logarithmic function (y = \log u) is one - to - one, if (\log\frac{x^{2}}{3}=\log3), then (\frac{x^{2}}{3}=3).

Step4: Solve for (x)

Multiply both sides of the equation (\frac{x^{2}}{3}=3) by 3 to get (x^{2}=9). Then take the square root of both sides: (x=\pm3). But since the domain of the logarithmic function (y = \log x) is (x>0), we discard (x = - 3).

Answer:

(x = 3) or (x=3) (the single valid solution is (x = 3))