How do you solve #2log_5x – log_5 2 = log_5 (2x+6)#?
We'll have to use a few properties of logs here, namely:
Luckily, all of are logarithms are base 5, so we can apply all the above properties. Using property ii on
Our equation is now
Using property i on this equation, this simplifies to:
Because both logs have the same bases, we can say:
This is a quadratic equation which is easily solved:
Two solutions...now what? Well, logarithms are defined only for