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Exponential function

y = ax . a > 1
 
Domain R; Range (0, ∞); Nature non-periodic, one-one, neither odd nor even, monotonically increasing, (a > 1); monotonically decreasing, (0 < a < 1)
 
78111.png
 
78105.png

Logarithmic function

Logarithmic function is inverse of exponential function.Hence domain and range of the logarithmic functions are range and domain respectively of exponential functions. Also graph of a function can be obtained by taking the mirror image of the graph of the exponential function in the line y = x.
 
y = loga x, a > 0 and ≠ 1
 
Domain (0, ∞); Range (–∞, ∞); Period non–periodic; Nature neither odd nor even; Interval which the inverse can be obtained (0, ∞)
 
 78099.png
 
78093.png

Properties of logarithmic function

  1. loga(x y) = logax +logay
  2. loga(x/y) = logax –logay
  3. loga (xb) = blogax
  4. 78087.png
  5. If logax > logay 78080.png
  6. If logax > y 78073.png
  7. 78066.png
  8. logyx = 78060.png




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