How do I solve for x?
log3(x+9)+log3(x-9)=1

Question

mathteacher1729 · Answer

The left side of the equation can be re-written as $\log_3(x^2-81)$. 

Now solve $\log_3(x^2-81) = 1$ using the fact that $\log_3(3) = 1$

anonymous · Answer

write the sum of the logs as the log of the product$$\log_{3}[(x+9)(x-9)]=1 $$then use the def of log to write$$3^1=(x+9)(x-9)$$now solve the polynomial$$x^2-81=3$$$$x=\pm \sqrt{84}$$=pm 2 sqrt{21}

anonymous · Answer

posted prematurely$$= \pm 2 \sqrt{21}$$both of these have to be checked for domain$$\sqrt{84} \approx 9.16$$so the negatove one must be discarded;

the solution set is $$\left\{ 2 \sqrt{21} \right\}$$

anonymous · Answer

ok...thanks for clearing that part up

anonymous · Answer

ur welcome; I accidentally posted and would have got to it all at once; i seem to be all thumbs tonight :{

anonymous · Answer

been there....thanks again :D

anonymous · Answer

:})