At the level of math that you are trying to work at, you have to be very careful about notation.
log_4(x) means \(\displaystyle log_4(x).\)
log4x means either \(\displaystyle log_{10}(4x)\) or \(\displaystyle ln(4x).\)
Here is a very basic rule that will help you with many log and exponential hint for equations:
\(\displaystyle log_a(x) = b \iff x = a^b.\)
log_4(x) means \(\displaystyle log_4(x).\)
log4x means either \(\displaystyle log_{10}(4x)\) or \(\displaystyle ln(4x).\)
Here is a very basic rule that will help you with many log and exponential hint for equations:
\(\displaystyle log_a(x) = b \iff x = a^b.\)