**Logarithm Solved Examples - Page 3**

** Logarithm Important Questions - Page 4**

** Logarithm Video Lecture - Page 5**

Logarithm, in mathematics is the exponent or power to which a stated number called base , is raised to yield a specific number. For example on the expression , the Logarithm of 100 to the base 10 is 2. This is written as Logarithms were originally invented to help simplify the arithmetical processes of multiplication, division, expansion to a power and extraction of a 'root', but they are now a days used for variety of purposes in pure and applied mathematics.

If for a positive real number (a ≠ 1) , , then the index m is called the Logarithm of b to the base a.

We write this as:

Log begins the abbreviation of the word ‘Logarithm’. Thus

Where = b is called the exponential form and is called the Logarithmic form.

**Exponential Form**

**Logarithmic Form
**

## Logarithm Shortcut Method and Formulas

**Product Formula:**The Logarithm of the product of two numbers is equal to the sum of their Logarithms.

i.e.

Generalisation: In general, we have

**Quotient formula**: The Logarithm of the quotient of two numbers is equal of their Logarithm.

i.e. . Where a, m, n are positive and a ≠ 1**Power formula**: The Logarithm of a number raised to a power is equal to the power multiplied by Logarithm of the number.

i.e. . Where a, m are positive and a ≠ 1**Base changing formula:**Where m, n, a are positive and n ≠ 1, a ≠ 1.**Reciprocal Relation:**, where a, b are positive and not equal to 1- , where a and x are positive and a ≠ 1
- If a > 1 and x > 1, then x > 0.
- If 0 < a < 1 and 0 < x < 1, then x > 0.
- If 0 < a < 1 and x > 1, then then x > 0.
- if a > 1 and 0 < x < 1, then then x < 0.
- Logarithm of 1 to any base is equal to zero. i.e. 1 = 0, where a > 0, a ≠ 1
- Logarithm of any number to the same base is 1. i.e. a = 1, where a > 0, a ≠ 1
**Common logarithms:**There are two base of logarithms that are extensively used these days. One is base e(e=2.71828 approx) and the other is base 10. The logarithms to base 10 are called the common logarithms.

AND

## Logarithm Solved Questions

**Example 1:**

**Answer: 3
**

**Solution:**

**Example 2: **If find yz(2 - x).

**Answer: 1**

**Solution:** yz(2 - x) = 2yz - xyz =

**Example 3:**

**Answer: 1
Solution:** Each is equal to k

log x = k(l + m - 2n),

log y = k(m + n - 2l), log z = k(n + l - 2m),

log xyz = k(0) xyz = = 1 = = 1

**Example 4: **If log

**Answer: 23
Solution:**

x + y =

**Example 5:** If log (x + y) = log , then log x - log y =

**Answer: Log 5
Solution:** x + y =

log x - log y = log 5

## Logarithm Questions from Previous Year Exams.

- Logarithm Aptitude

## Logarithm Online Study Material - Video Tutorial

## 0 Comments