f(x) = ax
f’(x) = a x log a
\(\because\) f(x) is increasing on R.
\(\therefore\) f’(x) > 0
\(\therefore\) a x log a > 0
\(\because\) Logarithmic function is defined for positive values of a.
\(\therefore\) a > 0
\(\therefore\) ax > 0
\(\because\) ax log a > 0
\(\therefore\) It can be possible when log ax > 0 & log a > 0 or ax < 0 & log a < 0.
log a > 0
\(\therefore\) a > 1
Hence, f(x) is increasing when a > 1.