SOLUTION: My sister needs help with this equation and since I am the big sister that knows all, I need help with it... log(x^2-2)+2log6=log6x the "logs" are all base b, if that makes

Question 126339: My sister needs help with this equation and since I am the big sister that knows all, I need help with it...
log(x^2-2)+2log6=log6x
the "logs" are all base b, if that makes a difference...
Thanks much
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Assume it is:
log(x^2 - 2)+ 2log(6) = log(6x)
:
log(x^2 - 2) + log(6^2) = log(6x); log/exponent equivalent
:
log(x^2 - 2) + log(36) = log(6x)
:
log(36(x^2-2)) = log(6x); adding logs same as multiplying
:
Equal logs: equal values:
36(x^2 - 2) = 6x
:
36x^2 - 72 = 6x; multiply what's inside the brackets
:
36x^2 - 6x - 72 = 0; Arrange as a quadratic equation
:
6x^2 - x - 12 = 0; simplified, divided eq by 6
:
This will factor to:
(3x + 4)(2x - 3) = 0
:
3x = -4
x =
and
2x = +3
x =
;
You can substitute both solutions in the original equation to check it:
:
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