Problem

$\log _{3} 3 x+\log _{9} x=4$

Answer

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Answer

\(\boxed{x = \sqrt{\frac{10^4}{3}}}\)

Steps

Step 1 ：\(\frac{\log_{10} 3x}{\log_{10} 3} + \frac{\log_{10} x}{\log_{10} 9} = 4\)

Step 2 ：\(\log_{10}(3x \cdot x) = 4\)

Step 3 ：\(\log_{10}(3x^2) = 4\)

Step 4 ：\(3x^2 = 10^4\)

Step 5 ：\(x^2 = \frac{10^4}{3}\)

Step 6 ：\(x = \pm \sqrt{\frac{10^4}{3}}\)

Step 7 ：\(\boxed{x = \sqrt{\frac{10^4}{3}}}\)

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