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Question

$log subscript 3 end subscript invisible function application left curly bracket 5 plus 4 log subscript 3 end subscript invisible function application open parentheses x minus 1 close parentheses right curly bracket blank equals 2 comma$ then $x$ is equal to

2
4
8
$\log_{2} 16$

The correct answer is: 4

We must have $x minus 1 greater than 0 rightwards double arrow x greater than 1 blank open parentheses i close parentheses$
and $5 plus 4 log subscript 3 end subscript invisible function application open parentheses x minus 1 close parentheses greater than 0 rightwards double arrow 4 log subscript 3 end subscript invisible function application open parentheses x minus 1 close parentheses greater than negative 5$
$rightwards double arrow log subscript 3 end subscript invisible function application open parentheses x minus 1 close parentheses greater than negative fraction numerator 5 over denominator 4 end fraction$
$rightwards double arrow x minus 1 greater than 3 to the power of negative 5 divided by 4 end exponent rightwards double arrow x greater than 1 plus 3 to the power of negative 5 divided by 4 end exponent blank open parentheses i i close parentheses$
From Eqs. (i) and (ii), we get $x greater than 1 plus 3 to the power of negative 5 divided by 4 end exponent.$ Therefore, $5 plus 4 blank log subscript 3 end subscript invisible function application open parentheses x minus 1 close parentheses equals 9 rightwards double arrow 4 log subscript 3 end subscript invisible function application open parentheses x minus 1 close parentheses equals 4$
$rightwards double arrow log subscript 3 end subscript invisible function application open parentheses x minus 1 close parentheses equals 1 rightwards double arrow x minus 1 equals 3 rightwards double arrow x equals 4$

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