Question

${3}^{x + 3} + {3}^{x - 1} = 41$
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Answer 1

${3}^{x + 3} + {3}^{x - 1} = 41 \\ {3}^{x}. {3}^{3} + \frac{ {3}^{x} }{3} = 41$

$y = {3}^{x}$

$y. {3}^{3} + \frac{y}{3} = 41 \\ 27y + \frac{y}{3} = 41 \\ \frac{81y + y = 123}{3}$

$82y = 123 \\ y = \frac{123}{82} \\ y = \frac{3}{2}$

${3}^{x} = y \\ {3}^{x} = \frac{3}{2} \\ x = log_{3}( \frac{3}{2} ) \\ x = 1 - log_{3}(2)$