Logarithms Rules

Monday, March 7, 2022

Logarithms Rules

There are 7 Logarithm rules which are useful in expanding Logarithm, contracting Logarithms, and solving Logarithmic equations. The seven rules of Logarithms are discussed below:

1. Product Rule

\log_{b} (P \times Q) = \log_{b} P + \log_{b} Q

The Logarithm of the product is the total of the Logarithm of the factors.

2. Quotient Rule

\log_{b} (\frac{P}{Q}) = \log_{b} P - \log_{b} Q

3. Power Rule

\log_{b} (P^{Q}) = q \times \log_{b} P

4. Zero Rule

\log_{b} (1) = 0

The Logarithm of 1 such that b greater than 0 but b≠1, equals zero.

5. The Logarithm of a Base to a Power Rule

\log_{b} b^{y} = y

The Logarithm of a base to a power rule states that the Logarithm of b with a rational exponent is equal to the exponent times its Logarithm.

6. A Base to a Logarithm Power Rule

b^log^y = y

The above rule states that raising the Logarithm of a number to the base of a Logarithm is equal to the number.

7. Identity Rule

log y y = 1

Basic Logarithm Formula

Some of the Different Basic Logarithm Formula are Given Below:

$\log_{b} (m \times n) = \log_{b} m + \log_{b} m$
$\log_{b} (\frac{m}{n}) = \log_{b} m - \log_{b} n$
$\log_{b} (x^{y}) = y \times \log_{b} x$
$\log_{b} \sqrt[m]{n} = \log_{b} n^{\frac{1}{m}}$
$m \log_{b} (x) + n \log_{b} (y) = \log_{b} (x^{m} y^{n})$

Addition and Subtraction

$\log_{b} (m + n) = \log_{b} m + \log_{b} (1 + \frac{n}{m})$
$\log_{b} (m - n) = \log_{b} m + \log_{b} (1 - \frac{n}{m})$

Change of Base Formula

In the change of base formula, we will convert the Logarithm from a given base ‘n’ to base ‘d’.

log n m = log d m log d n

log b (P Q) = q \times log b P

4. Zero Rule log b (1) = 0

5. The Logarithm of a Base to a Power Rule log b b y = y

6. A Base to a Logarithm Power Rule b log y = y 7. Identity Rule log y y = 1

Online Daily Study Material for Class I To, X, XII - R.Kr. Institute

Monday, March 7, 2022