When the independent variables of a function are exponents, the function is called exponential. Conversely, when the independent variable is an argument of the logarithm function, the function is said to be logarithmic.
Properties of exponents
For all real x and y where a and b > 0:
axay = ax+y ax/ay = ax-y (ab)x = axbx (a/b)x = ax/bx (ap)x = apx
The natural exponential base e is an irrational number defined as:
e = lim (1 + 1/n)n ≈ 2.718281828459045...
n -> ∞
Examples:
f(x) = 2x f(x) = 1 - e-x
Properties of logarithms
For m and n both positive real numbers where a > 0:
loga 1 = 0 loga a = 1 loga mp = p loga m loga mn = loga m + loga n loga m/n = loga m - loga n
A logarithm with base a can be converted to another base b using the formula:
logb x
loga x = --------
logb a
Relation between exponential and logarithmic terms
loga ax = x aloga x = x
13.1. Exponential functions
13.2. Applications of exponential functions
13.3. Logarithmic functions
13.4. Applications of logarithmic functions
13.5. Exponential and logarithmic equations
13.6. Solved problems