How do you solve $log_6x+log_6(x-9)=2$ ?

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Answer 1 · 2016-07-24T03:31:30

Use the log property $log_a(n) + log_a(m) = log_a(n xx m)$ :

$=>log_6(x(x - 9)) = 2$

$=>log_6(x^2 - 9x) = 2$

$=>x^2 - 9x = 6^2$

$=>x^2 - 9x = 36$

$=>x^2 - 9x - 36 = 0$

$=>(x - 12)(x + 3) = 0$

$=>x = 12 and -3$

Checking in the original equation, we find that only $x = 12$ works. Hence, the solution set is ${12}$ .

Hopefully this helps!

How do you solve log_6x+log_6(x-9)=2log_6x+log_6(x-9)=2?