Question

$if \: log_{9}(x) + log_{3}(x) = 3 \: \: then \: x =$
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Answer 1

Step-by-step explanation:

$log_{9}(x) + log_{3}(x) = 3 \\ log_{ {3}^{2} }(x) + log_{3}(x) = 3 \\ \frac{ log(x) }{ log(3 ^{2} ) } + log_{3}(x) = 3 \\ \frac{ log(x) }{2 log(3) } + log_{3}(x) = 3 \\ \frac{1}{2} log_{3}(x ) + log_{3}(x) = 3 \\ log_{3}( {x}^{ \frac{1}{2} } ) + log_{3}(x) = 3 \\ log_{3}( {x}^{ \frac{3}{2} } ) = 3 \\ {x}^{ \frac{3}{2} } = {3}^{3} \\ {x}^{ \frac{3}{2} } = 27 \\ {(x {}^{ \frac{3}{2} } })^{ \frac{1}{3} } = {27}^{ \frac{1}{3} } \\ {x}^{ \frac{1}{2} } = 3 \\ ({x}^{ \frac{1}{2} }) {}^{2} = {3}^{2} \\ x = 9$