# CLASS-9LAWS OF LOGARITHMS

Laws of Logarithm

1)  logₐ (mn) = logₐ m + logₐ n             (Product Law)

m

2)  logₐ (------) =  logₐ m – logₐ n       (Quotient Law)

n

3)  logₐ (mⁿ) =  n (logₐ m)                  (Power Law)

4)  logₐ a = 1

5)  logₐ 1 = 0

6)  logₐ aˣ = x

As, logₐ aˣ = x,

=>  a = x.1 = x

a⁴ X b²

Example.)  If,  y = ----------, then log y = 4 log a + 2 log b – 3 log c

c³

Common Logarithms

The logarithm to base 10 is called common logarithm. We denote log₁₀ m by log m only.

Example:  i)  (10)¹ = 10

=>     log₁₀ 10 = 1

=>     log 10 = 1

=>     log (10)¹ =  1             (Ans.)

Example: ii)   (10)² = 100

=>    log₁₀ 100 = 2

=>    log 100 = 2

=>    log (10)² = 2

Thus, log (10)¹ = 1, log (10)² = 2, etc       (Ans.)

Example: iii)  (10)ˉ¹ = - 1,

=>   log₁₀ (10)ˉ¹ = - 1

=>   log 10 = - 1

=>   log (10)ˉ¹ = - 1            (Ans.)

Example: iv)  (10)ˉ² = - 2

=>    log₁₀ (10)ˉ² = - 2

=>    log 10 = - 2

=>    log (10)ˉ² = - 2        (Ans.)

If no base is given, the base is always taken as 10,

as a example log 5 = log₁₀ 5,                                                                  log 7 = log₁₀ 7