Originally Posted by

**JennyFlowers** I must solve the following logarithmic equation:

$\displaystyle

log_{4}(2x+1) = log_{2}(x-3)-log_{4}(x+5)

$

I found the answer as:

$\displaystyle x = \frac{-17\pm\sqrt{305}}{2}$

Which gives me two approximate answers:

0.232 and -17.232

The negative answer clearly cannot be considered a solution. But what about the positive answer? When I sub it back into the original equation, it appears to cause a problem at $\displaystyle log_{2}(x-3)$ since it would give this log a negative argument. However, since it can be converted to $\displaystyle log_{4}(x-3)^2$ does that mean that 0.232 does work as a solution?

No. The argument of the real logarithm to any base must be positive, no matter if you raise to the second or to the 14th power, and this means your equation has no solution

Tonio

Thank you!