# CLASS-9INTRODUCTION OF LOGARITHM

LOGARITHMS

Logarithm is a most essential part of mathematics, and through this, we can solve very complicated calculations over time. It’s very logical and fun too. Now we will learn the logarithm in a reasonable and easy way.

a) Logarithmic form vis-à-vis exponential form, interchanging.

b) Laws of logarithms and their uses –

Expansion of expression with the help of laws of logarithm

a⁵ X b⁶

y = -----------

c⁷

log y = 5 log a + 6 log b – 7 log c

let a be a real number such that a > 0, and a ≠ 1, and let ‘b’ be a rational number such that aᵇ = x

then, b is called the logarithm of x to the base a, written as logₐ x

thus, aᵇ = x

b = logₐ x

Here, aᵇ is called the exponential form and logₐ x is called the logarithmic form.

Example.1)   2⁵ = 32

=>  log₂ 32 =  5         (Ans.)

Example.2)  10⁷ =  10000000

=>  log₁₀ 10000000 = 7    (Ans.)

Example.3)   9⁴ = 6561

=>  log₉ 6561 =  4        (Ans.)

1

Example.4)    3ˉ⁴ = -------

81

1

=>  log₃ (-------) =  - 4        (Ans.)

81

Logarithms of only positive real numbers are defined.