Question

What are the solutions to
log3x + log3(x2 + 2) = 1 + 2log3x?

x = –2

x = –1

x = 1

x = 2

There is no true solution.

Answer 1

use the properties of logs

log a + log b = log a×b

Answer 2

\[\log_{3} x+\log_{3} (x^2+2)=1+2\log_{3} x\]
\[\log_{3} x-2\log_{3} x+\log_{3} (x^2+2)=1\]
\[-\log_{3} x+\log_{3} (x^2+2)=\log_{3} 3\]
\[\log_{3} \frac{ x^2+2 }{ x }=\log_{3} 3\]
\[\frac{ x^2+2 }{ x }=3\]
\[x^2+2=3x\]
\[x^2-3x+2=0\]
?