Question 1029334
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solve 2log X- log(X-2) =2 log 3
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<pre>
2*log(x) - log(x-2) = 2*log(3)  --->

{{{log((x^2))}}} - {{{log((x-2))}}} = {{{log((3^2))}}}  --->

{{{log((x^2/(x-2)))}}} = {{{log((9))}}}  --->

{{{x^2/(x-2)}}} = {{{9}}},           (next step is to multiply both sides by (x-2) to rid off the denominator)

{{{x^2}}} = {{{9*(x-2)}}}         (next step is to simplify)

{{{x^2 - 9x + 18}}} = {{{0}}},       (next step is to factor the left side)

(x-3)*(x-6) = 0.

The roots of the last equation are  x = 3  and  x = 6.

They both satisfy the original equation. Check it !

<U>Answer</U>.  x = 3  and  x = 6.
</pre>