Graph of Logarithmic function when `0lt base lt1`

Graph of Logarithmic function when base >1

Graph of Exponential function for 0< base <1

Logarithmic function and graph ( case 1 - base >1 and Case 2- base <1)

Statement -1: 0 lt x lt y rArr "log"_(a) x gt "log"_(a) y,"where" 0 lt a lt 1 Statement-2: "log"_(a) x is a decreasing function when 0 lt a lt 1.

Draw the graphs of the logaritmic functhmic functions. (i) log_(a)x , " when a gt 1 (ii) log_(a)x, " when " 0 lt a lt 1

Draw the graph of the function and discuss the continuity and differentiability at x = 1 for, f(x) = {{:(3^(x)",","when",-1 le x le 1),(4-x",","when",1 lt x lt 4):}

Solve the inequation : 0lt x/3 lt1

Let f be a non-negative function defined on the interval [0,1] . If int_0^xsqrt(1-(f\'(t))^2)dt=int_0^xf(t)dt, 0lexle1 and f(0)=0 , then (A) f(1/2)lt1/2 and f(1/3)gt1/3 (B) f(1/2)gt1/2 and f(1/3)gt1/3 (C) f(1/2)lt1/2 and f(1/3)lt1/3 (D) f(1/2)gt1/2 and f(1/3)lt1/3