What is the domain and range of #y = log2^x#?

1 Answer
Dec 13, 2017

Answer:

Range: # y in RR#
Domain: # x in RR#

Explanation:

To answer this question we must consider our log laws:

# alphalogbeta = logbeta^alpha #

So using the knowledge:

#y = log2^x => y = xlog2 #

Now this is just linear!

We know #log2 approx 0.301#

#=> y = 0.301x #

Now we see by a sketch:

graph{y = 0.301x [-10, 10, -5, 5]}

That all #x# and all #y# are defined, yielding:

#x in RR # and # y in RR #