Answer:
[tex]x = 45 \sqrt{5} [/tex]
Step-by-step explanation:
[tex] {3}^{2 log_{3}(x) + log_{3}(5) } = {3}^{ 4log_{3}(15) } [/tex]
[tex] {3}^{ log_{3}( {x}^{2} ) } {3}^{ log_{3}(5) } = {3}^{ log_{3}( {15}^{4} ) } [/tex]
[tex]5 {x}^{2} = {15}^{4} [/tex]
[tex] {x}^{2} = \frac{ {15}^{4} }{5} [/tex]
[tex]x = \frac{ {15}^{2} }{ \sqrt{5} } ( \frac{ \sqrt{5} }{ \sqrt{5} } )[/tex]
[tex]x = \frac{ {15}^{2} \sqrt{5} }{5} = 45 \sqrt{5} [/tex]
