Logarithm of numbers (Index & Logarithmic Form)

The logarithm to base a of a number P, is the index x to which a must be raised to be equal to P.

Thus if P = a^x, then x is the logarithm to the base aof P. We write this as x = log a P. The relationship log_aP = x and a^x=P are equivalent to each other.

a^x=P is called the index form and log_aP = x is called the logarithm form

Easy way to learn Logarithm Basics Click interactive slideshow

https://www.slideshare.net/slideshow/embed_code/key/eKcMhM60XKWiyBLogarithm from Bangladesh University of Professionals

Conversion From Index to Logarithmic Form

Write each of the following index form in their logarithmic form

1. a) 2⁶ = 64 b)            25^1/2 = 5                               c)  4⁴= 1/256

Solution

1. a) 2⁶ = 64

Log₂ 64 = 6

1. b) 25^1/2 = 5

Log₂₅5=1/2

1. c) 4^-4= 1/256

Log₄1/256 = -4

Conversion From Logarithmic to Index form.

1. a) Log₂128 = 7 b)            log₁₀ (0.01) = -2
2. c) Log₅ 2.25 = 2

Solution

1. a) Log₂128 = 7

2⁷ = 128

1. b) Log₁₀(0.01) = -2

10^-2= 0.01

1. c) 5 2.25 = 2

1.5² = 2.25