How to do this?

Question

$log_3 (x-2) = 3-log_3(x+4)$

1481 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-10T14:23:44

Rearranging gives:

$log_3(x-2)+log_3(x+4)=3$
which is equivalent to:
$log_3[(x+2)(x+4)]=3$

Since if $N=a^x$ then $log_aN=x$
$(x+2)(x+4)=3^3=27$
expanding:
$x^2+6x+8=27$
$x^2+6x-19=0$
$x=-(b+-sqrt(b^2-4ac))/(2a)$

so $x=(-6+-sqrt(36+76))/(2)$
x=2.29 or-8.29