Question

Solve for x:

Answer 1

x:\[\log_{3}(x^2-4)-\log_{3}(x+2)=2 \]

Answer 2

remember
\[\log a - \log b = \log \frac{ a }{ b }\]
and
\[\log a + \log b = \log (a \times b)\]

Answer 3

so how would you change

\[\log _{3} (x^2 -4 ) - \log _{3} (x+2) = ????\]

Answer 4

First we combine logarithms

Answer 5

(log(x^2-4))/(log(3))-(log(x+2))/(log(3)) = (log(1/(x+2)))/(log(3))+(log(x^2-4))/(log(3)) = (log(1/(x+2))+log(x^2-4))/(log(3)) = (log((x^2-4)/(x+2)))/(log(3)):
(log((x^2-4)/(x+2)))/(log(3)) = 2

Answer 6

Then we multiply both sides by a constant to simplify the equation.
Multiply both sides by log(3):
log((x^2-4)/(x+2)) = 2 log(3)

Answer 7

Then we simplify logarithmic terms on the right hand side.
2 log(3) = log(3^2) = log(9):
log((x^2-4)/(x+2)) = log(9)