How do you find the domain and range of $y = {log}_{5} x$ $y = log_5x$ ?

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How do you find the domain and range of $y = {log}_{5} x$ $y = log_5x$ ?

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Answer 1 · 2015-07-19T13:04:45

$f (x) = {log}_{5} x$ $f(x) = log_5 x$ is the inverse of the function $e (x) = 5^{x}$ $e(x) = 5^x$
which has domain $(- \infty, \infty)$ $(-oo, oo)$ and range $(0, \infty)$ $(0, oo)$ .

So the domain of ${log}_{5} x$ $log_5 x$ is $(0, \infty)$ $(0, oo)$ and range is $(- \infty, \infty)$ $(-oo, oo)$

Explanation:

The domain of $e (x) = 5^{x}$ $e(x) = 5^x$ is the whole of $RR$ , that is $(-oo,oo)$ , but its range is $(0, oo)$ .

So the domain of its inverse $y = log_5 x$ is $(0,oo)$ and its range is $(-oo,oo)$

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How do you find the domain and range of $y = {log}_{5} x$ $y = log_5x$ ?

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