Now (a x)y = exp(y ln(a x )) = exp(y x ln(a )) = a yx = a xy Therefore
(a x)y = a xy (Exponential of an exponential)
Now a xay = exp(x ln(a)) · exp(y ln(a) = exp(x ln(a)+y ln(a)) = exp( (x +y )ln(a) ) = a x+y Therefore has the exponential property
a xay = a x+y for all real numbers x and y when a > 0.
Now for the natural number e = exp(1) = 2.718281828… (irrational, deci), the natural logarithm of e, ln (e) = 1 Therefore
e x = exp( x) for all real x when a > 0
as a x = exp( x ln(a)). Calculators often have a button marked e x for the evaluation of the exponential function exp( x)
Caution: the capital EXP on some calculators will not help you with the calculation of exp(x). Use the button marked e x instead.