# Tips And Tricks And Shortcut For Logarithm

## Tips and Tricks and Shortcuts to solve Logarithm:-

The first question which arises in our mind is What is Logarithm?

Definition

The logarithm is the inverse function of exponentiation.

logarithm is a power to which a number must be raised to get another number.
Logarithm was introduced by John Napier in the early 17th century to simplify calculations.
A logarithm is of two types:-

• Common Logarithm
• Natural Logarithm

Common Logarithm- Logarithm with base 10 is Common logarithm.

Natural Logarithm-  Logarithm with base e is Natural Logarithm.

Example of Logarithm

log 100 = 2
because
102 = 100
A natural logarithm is written,

Let’s have a look on some question that will help better in understanding Logarithm.

## Logarithm Tips and Tricks and shortcuts

### Question 1

Which of the following statement is not correct?

Option

A) log (1 + 2 + 3) = log 1 + log 2 + log 3
B) log( 2+3) = log (2×3)
C) log10 1 = 0
D) log10 10 = 1

#### Explanation

a)  log( 1+2+3) = log6 = log (1×2×3) = log1+ log2+log3

b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3

log (2 + 3) ≠ log (2 x 3)

c) Since,  loga 1=0,

so log10 1 = 0

d) Since, loga a = 1
so, log10 10 = 1

### Question 2

If X is an integer then solve(log2 X)2– log2x4-32 = 0

Option

A) 256
B) 125
C) 375
d) None of these

#### Explanation

Let us consider,(log2 X)2– log2x4-32 = 0 —— equation 1

let log2 x= y
equation 1 = y2– 4y-32=0
y2-8y+ 4y – 32= 0
y(y-8) + 4(y-8) =0
(y-8) (y+4)= 0
y=8, y= -4
log2=8 or, log2X = -4
X= 28 = 256, 0r 2-4 = $\frac{1}{16} \$
Since, X is an integer so X = 256

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