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what does "solve" mean in this context?
Whoops! Not solve. Just graph and find the domain/range
I would use a graphing calculator like desmos https://www.desmos.com/calculator to graph this out. You will have to use the change of base formula to make sure the expression is typed in properly you will have to type in log(x+2)/log(3) - 1
Ok thanks :) Would the domain be all real numbers?
why all real numbers?
you should have this graph https://www.desmos.com/calculator/fs1pnhr9hx
the left side of the graph seems to hit a "wall" of some sort
Ok, now I do. And it does seem like that
it turns out that you cannot plug in 0 or negative numbers into a log function so x+2 has to be positive x+2 > 0 leads to x > ???
x=-2 ? x+2=0
yeah x = -2 is your vertical asymptote. The graph does NOT touch the vertical asymptote. It only gets closer and closer and closer.
solving x+2 > 0 for x gives x > -2, which is the domain
Alright, I see :) Now what about the range?
the left side shoots off to negative infinity (very quickly) the right side slowly approaches positive infinity. it just keeps growing forever
so the range would be all real #'s or infinity
all real numbers I think you're thinking of this notation \(\Large (-\infty,\infty)\)