Thread: Can someone help me solve this logarithmic equation?

Can someone help me solve the attached logarithmic equation?

Rewrite 3 as $\displaystyle log_2(8)$

$\displaystyle log_2(x+3) + log_2(x-4) - log_2(8) = 0$

Using the laws of logs combine into one log

$\displaystyle log_2(\frac{(x+3)(x-4)}{8}) = 0$

Remove the log:

$\displaystyle \frac{(x+3)(x-4)}{8} = 1$

and solve

I get x = 5 and x = -4 but the solution guide rejects the x = -4. Is this because plugging in the value of -4 into the logarithmic expression is not possible or as the calculator would "error?"

Originally Posted by s3a

I get x = 5 and x = -4 but the solution guide rejects the x = -4. Is this because plugging in the value of -4 into the logarithmic expression is not possible or as the calculator would "error?"

-4 is rejected because there are no real solutions to a negative logarithm. Since all logs must be greater than 0 only x=5 is a solution