Logarithm - Arithmetic Aptitude Questions and Answers

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Logarithm - Important Formulas

Logarithm:

If a is a positive real number, other than 1 and a^m = x, then we write:
m = log_ax and we say that the value of log x to the base a is m.

Examples:

(i). 10³ 1000 log₁₀ 1000 = 3.

(ii). 3⁴ = 81 log₃ 81 =

(iii) 2^-3 = $\frac { 1 } { 8}$ log₂ $\frac { 1 } { 8}$ = -3

(iv) (.1)² = .01 log_(.1) .01 = 2.

2.Properties of Logarithms:

1. log_a (xy) = log_a x + log_a y

2. log_x x = 1

3 .log_a 1 = 0

4. log_a (xⁿ) = n(log_a x)

5. log_{a $[ \frac { x } { y } ]$ =}log_a x - log_a y

6 . log_a x = $\frac { logb X } { logb a}$ = $\frac { log X } { log a}$

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