We already know several laws of indices, for example ${\left(x^a\right)}^b$ = x^{ab}$, and now we need to learn their corresponding laws of logarithms. In fact, every law of indices gives us a law of logarithms, which makes sense because logarithm is the inverse of exponentiation.

The first we need to learn is

This basically says that we can bring powers out of the logarithm. There is one very important detail, though, which will be explained in the first example.

Solve the equations, giving your answers to $3$ significant figures:

1. $$4\times {\left(\frac{2}{5}\right)}^x=9$$
2. $$2^{2x+5}=3^{2x+14}$$