Let a
^{m} = x. Then m = log
_{a} x. (a = positive real number)
Let 2
^{6} = 64. Then 6 = log
_{2} 64.
Logarithm is a kind of operation,
m is the number of times where base number
a is multiplied by itself to reach number
x.
Properties of Logarithms 
Note 
log_{a} 1 = 0 
log of 1 to any base is 0. 
log_{x} x = 0 
log of any number to its own base is always 1. 
log 100 = 2 
default base is 10 known as common logarithm. 
log_{a} (xy) = log_{a} x + log_{a} y 

log_{a} (x/y) = log_{a} x  log_{a} y 

log_{a} x^{p} = p log_{a} x 

log_{a} x = 1/log_{x} a = log_{b} x / log_{b} a 

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