Question

how do you solve for x in this equation...ln (9-6 x) - 2ln x = ln 3

Answer 1

Make use of the following log properties:
\(\log(x)^n = n * \log(x)\)

\(\log(A) - \log(B) = \log(A/B)\)

If \(\log(A) = \log(B)\) then \(A=B\)

Answer 2

\[
\ln (9-6 x) - 2\ln x = \ln 3 \\
\ln (9-6 x) - \ln x^2 = \ln 3 \\
\ln((9-6x) / x^2) = \ln(3) \\
(9-6x) / x^2 = 3 \\
9-6x = 3x^2 \\
3x^2 + 6x - 9 = 0 \\
x^2 + 2x - 3 = 0 \\
\]Can you solve it now?

Answer 3

Yeah i got it thanks!

Answer 4

You are welcome.

Remember you cannot take logarithm of a negative number. If you get an x value that will end up taking log of a negative number discard that solution as extraneous solution.