How do you solve #log (x + 3) = log (6) - log (2x-1)#?
I'm assuming that all the
First of all, let's compute the domain of the logarithmic expressions.
For the first one,
For the last one, we get
As the second condition is the more restrictive one, we can assume that the domain is
Now, in order to "get rid" of the logarithmic expressions, it is necessary to simplify the terms on the right-hand side.
To do so, remember the logarithmic rule:
In our case, it means:
Now, due to the fact that for
... multiply both sides with
This is a quadratic equation that can be solved e. g. with the quadratic formula:
So, we have just one solution:
Hope that this helped!