Question
Find $x,$ if : $log_x(5x - 6) = 2$
✓
Answer
$log_x(5x - 6) = 2$
$\Rightarrow 5x - 6 = x^2 ...[$ Removing logarithm $]$
$\Rightarrow x^2 - 5x + 6 = 0$
$\Rightarrow x^2 - 3x - 2x + 6 = 0$
$\Rightarrow x( x - 3 ) - 2( x - 3 ) = 0$
$\Rightarrow ( x - 2 )( x - 3 ) = 0$
$\therefore x = 2, 3.$
$\Rightarrow 5x - 6 = x^2 ...[$ Removing logarithm $]$
$\Rightarrow x^2 - 5x + 6 = 0$
$\Rightarrow x^2 - 3x - 2x + 6 = 0$
$\Rightarrow x( x - 3 ) - 2( x - 3 ) = 0$
$\Rightarrow ( x - 2 )( x - 3 ) = 0$
$\therefore x = 2, 3.$
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