Logarithms  Aptitude basics, practice questions, answers and explanations 
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1.If x,a and m are any three numbers connected by the relation:

m=a^x     (a>0, a≠1),then,

“x” is defined as the logarithm of “m” to the base “a” and is written as:

x= log_a m

2.Some important results:

(a) m =a ^{log am}

(b) x =log _a (a^x)

(c) log _a 1 = 0

3.Some important theorems:

(a) log _a (mn) = log _a m + log _a n

(b) log _a (m/n) = log _a m – log _a n

(c) log _a (mⁿ) = n. log _a m

(d) log _a m = (log _b m) / (log _b a) ……. Change of base theorem

(e) log _a a  = 1

(f) log _a b * log _b a = 1