The solution of ${log}_{3} (5 + 4 {log}_{3} (x - 1)) = 2$ is

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Solution

Here base $\neq 1, > 0$
We have ${log}_{3} (5 + 4 {log}_{3} (x - 1)) = 2$
Which is equivalent to the equation,
$∴ 5 + 4 {log}_{3} (x - 1) = 3^{2} \Rightarrow {log}_{3} (x - 1) = 1 \Rightarrow x - 1 = 3^{1} ∴ x = 4$
Hence $x = 4$ is solution of the original equation.

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