Question

Use properties of logarithms and solve the equation. Check for extraneous solutions.
log(base3)(x+2) + log(base3)(x-2)=2

Answer 1

start with
\[\log_3((x+2)(x-2))=2\] then rewrite in equivalent exponential form as
\[(x+2)(x-2)=3^2\] and finally solve the quadratic

Answer 2

you get
\[x^2-4=9\]
\[x^2=13\] and so \[x=\sqrt{13}\]

Answer 3

Thank you!! So exponential form is the base of the first log, 3, to the power of what the initial equation equaled, 2?

Answer 4

yes, after you use the property that \(\log(A)+\log(B)=\log(AB)\) to write as a single log

Answer 5

for example \(\log_5(x+6)=4\iff x+6=5^4\)

Answer 6

Awesome! Thanks for your help!!

Answer 7

yw