There are several important techniques that allow us to solve equations using logarithms.

An essential thing to know is that whenever you see $\log$ written without a base, it is implied that the base is $10,$ so $\log (x)$ just means ${\log }_{10}(x).$

You probably have a button on your calculator with just 'log' on it, so this means ${\log }_{10}.$ The reason for this is that some equations can be solved by taking $\log$ of both sides, as we will see next.

Solve the equations

1. $${\log }_2(x+5)-{\log }_2(x-5)=-3$$
2. $$\log (x+2)+2\log (2)+\log (5)$$