Basics of Logarithm
A logarithm i s the opposite of a power. In other words if we take logarithm of a number, we undo thr exponentiation.
Logarithm is used to solve exponential problems. We define one type of logarimth called log base 2 and denoted by log with a subscript of 2. The log base is defined so that:
log base 2 c = k
so the solutio to the above is:
2^k = c
for any given number c. In other words, the logarithm gives the exponent as the output if you give it the exponentiation result as the input. To get all answers for the above problems. we just need to give the logaritm the exponentiation result c and it will give the right k of 2.
The solution to the above problems are:
log base 2 8 = 3
log base 2 4 = 2
log base 2 16 = 4
log base 2 1 = 0
The Laws of Logarithm
1. Product Rule Logb (M.N) = logb M + logb N
2. Quotient Rule Logb (M/N) = logb M - logb N
3. Power Rule Logb (M^k) = k . logb M =
4. Zero Rule Logb (1) = 0
5. Identity Rule Logb (b) = 1
6. Log of Exponent Rule Logb (b^k) = k
(Logarithm of Bsae to Power Rule)
7. Exponent of Log Rule bLogb (k) = k
(A Base to a Logarithm Power Rule)
Example of Logarithm Equation
log6 (2x - 4) + log6 (4) = log6 40
log6 4(2x - 4) = log6 40
log6 8x - 16 = log6 40
8x - 16 = 40
8x = 40 + 16
8x = 56
x = 56/8
x = 7