one to one property, 3^x-4=1/27 Need help do not understand

Answer 1

f(x) is 1:1 if every x produces a unique value of f, and every value of f can be produced by a unique value of x.

Geometrically, that means that no horizontal or vertical line cuts the graph more than once.

Graph this function, and you will see that it is 1:1.

However, what you have is an equation, whose solution is

x=log(4 1/27)/log(3)

Nothing 1-to-1 about solving an equation, unless you just want to show that there is a unique solution.