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.