Question

solve the above equation

Answer 1

Here's your answer.
${x}^{ log_{x}{(x + 3)}^{2}} = 16 \\ take \: log \: (base \: x) \: both \: sides \\ log_{x}(16) = log_{x}{(x + 3)}^{2} \\ \implies \\ 16 = {(x + 3)}^{2} \\ or \\ x + 3 = \pm \: 4 \\ \implies x = 1 \: or \: - 7$

Plugging in the values of x = 1 in the original equation does not satisfy it, but when x = -7, the equation does satisfy, so the answer will be x = -7.
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