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 $y in RR$

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