C3 transformation of lnx graph help :)

Hey i have been doing some revision and forgot how this came about:

i was trying to draw the graph y=ln(3-x)

which i know that its a reflection in the y axis due to the -x but doesn't the positive 3 mean a translation in the x axis which means it moves left by 3/ but the example in the book says it moves right by 3?!

am i missing something here?

thanks for help xxx

Am i missing something here?

thanks for help xxx

Yes, you are. The book is correct.

ln(3-x)

= ln (-(x-3))

So you are subtracting 3 from x and the graph is moved to the right.

See attached.

edit: You need to consider what has been done to the "x". The fact that there is a minus sign in front, is probably what confused the issue.

your graph cuts the axis at wrong coordinates in your attached image

when x=3 , y=0