Logarithm equation

[Loki123]

Where did I go wrong? The first picture is my attempt. The second picture is what the app suggests. I do not understand why we separate the equation into two cases, one where <=4 and one where => 4... Please explain that. Also If someone could help me understand why base needs to be >0 and not equal to 1. Thank you very much in advance.

 

[blamocur]

The base of a logarithm cannot be negative because raising negative numbers into real power is not really defined in the domain of real number (see the definition of logarithms).
And once you look closely at the definition of logarithms you might figure out why logarithms with base 1 are pretty meaningless too.
Let us know if you need more hints here.