With log base 4, solve log(2x+3) + log(2x+15) = 1 + log(14x+5)

How might one simplify this? It looks as though raising both sides to the power 4 is the way to go, but it is not immediately obvious how to do this. In order to get both sides into the form 'log of something', we need to apply log laws. A student familiar the log laws will see that we do this to the LHS by multiplying together the arguments. For the RHS, an additional step is required, to convert 1 into log(4) before doing this. (Note: it is only this step which makes the base of the log particularly relevant.) 

Once this has been done, and both sides raised to the power 4, it is simply a case of solving a quadratic, either by inspection (which is not terribly difficult), or using the quadratic formula.