C3 domain and range

Look at this: https://www.google.co.uk/search?q=ln(2x-1)&oq=ln(2x-1)&aqs=chrome..69i57j6j0l2.903j0j4&sourceid=chrome-mobile&ie=UTF-8

You typed it wrong

Find the range of ln(2x-1) xer x>0.5

Of course i usually manage to somehow guess the right range everytime.

i said xer for this and it's right but i'd like to know why

https://www.google.co.uk/search?q=ln2x-1&rlz=1C1PRFE_enGB694GB694&oq=ln2x-1&aqs=chrome..69i57.2364j0j1&sourceid=chrome&ie=UTF-8#q=ln(2x%2B1)+graph

Here's the graph of it but if x is limited to 0.5 then surely the graph doesn't even extend to anywhere past the first quadrant??? so whatever value comes out of shoving in 0.5 into the function. Yet you can have ln0 so i still don't get how this stuff works. Even though i've done all the jan papers

What do you mean?? You can't have ln(0)....

The function is clearly defined for $x>0.5$ and NOT $x\geq 0.5$ otherwise the function is undefined at $x=0.5$. The graph's asymptote is x=0.5 which it tends towards, and the range is all the reals as every possible real number can be obtained from the function.