Please help, how to solve: log4(x+1)=log4(4x-5)

The 4's after log is supposed to be smaller. Base, I think it is called.

log₄(x + 1) = log₄(4x - 5) implies that x + 1 = 4x - 5
Therefore x = 2

You take the opposite of log base 4 on each side:
4^(Log4(x+1))=4^(log4(4x-5)
BlogB(x) = x
So you ed up with x+1=4x-5
6=3x
x=2