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## Logarithmic Functions

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**Exponentiation:**The third power of some number ‘b’ is the product of 3 factors of ‘b’. More generally, raising ‘b’ to the n-th power (n is a natural number) is done by multiplying n factors. The idea of logarithms is to reverse the operation of exponentiation. Definition: If b≠1 and ‘y’ are any two positive real numbers then there exists a unique real number ‘x’ satisfying the equation bx = y. This x is said to be the logarithm of y to the base b and is written as Logb y = x**Thus**log3 9 = 2 since 32 = 9 log6 216 = 3 since 63 = 216 log10 0.01 = -2 since 10-2 = 0.01 Similarly x0 = 1 implies that logx 1 = 0 Note: • Since the exponential function value can never be zero, we can say that logarithm of zero is undefined. 2. Similarly, logarithmic function is not defined for negative values.**Types of logarithms:**• logarithms to base 10 are called common logarithms • logarithms to base 2 are called binary logarithms • logarithms to base ‘e’ are called natural logarithms • Identities:**y**Graph: y = x (0 , 1) y = ex y = loge x x (1 , 0)