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

Rearranging the equation gives:
\[\large \log_{3} (x^{2}+2)-\log_{3} x=1\ ............(1)\]
Using the following rule of logs on equation (1)
\[\large \log_{} a-\log_{} b=\log_{} \frac{a}{b}\]
we get:
\[\large \log_{3} \frac{x^{2}+2}{x}=1\ ...........(2)\]
Therefore
\[\large \frac{x^{2}+2}{x}=3\ .........(3)\]
Now you need to form a quadratic from equation (3) and solve it.

Answer 2

thanks!

Answer 3

You're welcome :)