Question

Which of the following is a solution to the equation log 4 x + log 4 (x – 3) = 1 ?

Answer 1

\[\log _4(x)+\log _4(x-3)=1\]

Answer 2

Using rule \(\large \log_a b=\frac{\log_cb}{\log_ca}\)
\[\frac{\log (x-3)}{\log (4)}+\frac{\log (x)}{\log (4)}=1\]
Combine
\[\frac{\log ((x-3) x)}{\log (4)}=1\]
Multiply both sides by log(4):
\[\log((x-3) x)=\log(4)\]
\[(x-3) x=4\]
\[x^2-3 x=4\]
\[x^2-3x-4=0\]
Solve