What is the domain and range of $y = {log}_{2} x$ $y=log_2x$ ?

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Answer 1 · 2017-07-31T12:18:03

Domain: $(0, \infty)$ $(0,oo)$

Range: $RR$

First, remember that you cannot take $log(0)$ and you cannot take the logarithm of a negative number and get a real number

So, $x>0 => x in (0,oo)$ which is our domain

Also, by the definition of $log_2x$

$y=log_2x$

$<=>$

$2^y=x$

which is defined for all real numbers $(RR)$ , which gives us our range

What is the domain and range of y=log_2xy=log2xy=log_2x?