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

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Answer 1 · 2017-12-13T16:43:25

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

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 #