To solve the equation [tex]\( 2 \log x - \log 3 = \log 3 \)[/tex], we proceed as follows:
1. Isolate the logarithmic term involving [tex]\( x \)[/tex]:
[tex]\[ 2 \log x - \log 3 = \log 3 \][/tex]
2. Solve for [tex]\( 2 \log x \)[/tex] by adding [tex]\( \log 3 \)[/tex] to both sides of the equation:
[tex]\[ 2 \log x = \log 3 + \log 3 \][/tex]
3. Combine the logarithms on the right-hand side using the property [tex]\(\log a + \log b = \log(a \cdot b)\)[/tex]:
[tex]\[ 2 \log x = \log(3 \cdot 3) \][/tex]
[tex]\[ 2 \log x = \log 9 \][/tex]
4. Divide both sides by 2 to solve for [tex]\( \log x \)[/tex]:
[tex]\[ \log x = \log 9 / 2 \][/tex]
[tex]\[ \log x = \log 9^{1/2} \][/tex]
5. Simplify the right-hand side to get [tex]\( x \)[/tex]:
[tex]\[ \log x = \log 3 \][/tex]
6. Since the logarithm is the same on both sides, we equate the arguments:
[tex]\[ x = 3 \][/tex]
So, the solution to the equation [tex]\( 2 \log x - \log 3 = \log 3 \)[/tex] is [tex]\( x = 3 \)[/tex].
Thus, listing the potential solutions from least to greatest:
[tex]\[ x = 3 \][/tex]
DONE
