Question #7cc9a

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Answer 1 · 2017-02-07T00:17:38

$x = 3$ $x=3$

$2 ln (x - 2) - ln (2 x - 5) = 0$ $2ln(x-2) - ln(2x-5) = 0$

$\Rightarrow ln ({(x - 2)}^{2}) - ln (2 x - 5) = 0$ $=> ln((x-2)^2) - ln(2x-5) = 0$

$\Rightarrow ln ({(x - 2)}^{2}) = ln (2 x - 5)$ $=> ln((x-2)^2) = ln(2x-5)$

$\Rightarrow e^{ln ({(x - 2)}^{2})} = e^{ln (2 x - 5)}$ $=> e^ln((x-2)^2) = e^ln(2x-5)$

$\Rightarrow {(x - 2)}^{2} = 2 x - 5$ $=> (x-2)^2 = 2x-5$

$\Rightarrow x^{2} - 4 x + 4 = 2 x - 5$ $=> x^2-4x+4 = 2x-5$

$\Rightarrow x^{2} - 6 x + 9 = 0$ $=> x^2 - 6x + 9 = 0$

$\Rightarrow {(x - 3)}^{2} = 0$ $=> (x-3)^2 = 0$

$:.x=3$