Logarithms

 

   Logarithm to a certain base of a number is equal to the power to which the base must be raised to give the number.

                  M = X^a

                  Log_x M = a

                 4 = 2² 

                 Log₂4 = 2

Evaluate the following logarithms

1.    Log₁₀  10000

2.    Log₄   1/16

3.    Log₁₀₀  0.00001

                                             Solution

1.     Log₁₀ 10000

X  = 10000              

10^x  =  10⁴

X  = 4

2.    Log₄ 1/16

X  =  log₄ 1/16

4^x  = 16^-1

2^2x  = (2⁴)^-1

2x  = -4

X  -4/2

X = -2

3.     Log₁₀₀  0.00001

X = log₁₀₀ 0.00001

100^x   = 10^-5

10^2x  = 10^-5

2x    = -5

X = -5/2