Mentor in Mathematics,
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.
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 logarith of y to the base b and is written as
Logb y = x
The idea of logariths is to reverse the operation of exponentiation.
log3 9 = 2 since 32 = 9
log6 216 = 3 since 63 = 216
log10 0.01 = -2 since 10-2 = 0.01
x0 = 1 implies that logx 1 = 0
Since the exponential function value can never be zero, we can say that logarith of zero is undefined.
2. Similarly, logarithic function is not defined for negative values.
logariths to base 10 are called common logariths
logariths to base 2 are called binary logariths
logariths to base ‘e’ are called natural logariths
Sol: Given that
y = loge x
y = ex