Question

prove that the logarithmic function is strictly increasing

Answer 1

Step 1:Let f(x)=logxf(x)=log⁡xDifferentiating w.r.t xx we get,f′(x)=1xf′(x)=1xStep 2:Clearly when f′(x)>0f′(x)>0⇒1x⇒1x>0>0 when x>0x>0Therefore f′(x)>0f′(x)>0Hence f(x)f(x) is an increasing function for x>0x>0(i.e) f(x)f(x) is increasing function whenever it is defined.