# 10) Prove that the logarithmic function is increasing on $( 0 , \infty )$

Let logarithmic function is log x
$f(x) = log x$
$f^{'}(x) = \frac{1}{x}$
Now, for all values of x in $( 0 , \infty )$ , $f^{'}(x) > 0$
Hence,  the logarithmic function $f(x) = log x$  is increasing in the interval  $( 0 , \infty )$

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