Quotient Rule of Logarithms
According to the quotient rule for logarithms, the logarithm of a division between two numbers is the subtraction of the logarithms of each number.
Specifically, the rule states that logb (m/n) = logb m – logb n. Let’s proceed to derive this rule.
Derivation Process:
Suppose logb m equals x and logb n equals y. We’ll express these in their exponential forms.
logb m = x implies m = bx … (1)
logb n = y implies n = by … (2)
When we divide equation (1) by equation (2),
m/n = bx / by
Applying the quotient rule for exponents,
m/n = bx – y
Converting back into logarithmic form,
logb (m/n) = x – y
By substituting back for x and y,
logb (m/n) = logb m – logb n
Thus, we have derived the quotient rule for logarithms. This rule can be utilized as follows:
log (y/3) = log y – log 3
log 25 = log (125/5) = log 125 – log 5
log7 (a/b) = log7 a – log7 b
It’s important to note that the quotient rule does not imply anything for log (m – n).
Related Topics:
Log Rules
Logarithm Rules or Log Rules are critical for simplifying complicated formulations that include logarithmic functions. Log Rules make it easier to calculate and manipulate logarithms in a variety of mathematical and scientific applications. Out of all these log rules, three of the most common are product rule, quotient rule, and power rule. Other than these, we have many rules of the logarithm, which we will discuss further in the article. This article explores, all the rules for logs including derivative and integral, in detail with the Logarithm Rules Examples. So, let’s start learning about all the rules logarithms have.
Table of Content
- What are Log Rules?
- Types of Logarithm
- List of Logarithm Rules
- Natural Log Rules
- Applications of Logarithm
- Product Rule of Logarithms
- Logarithm Power Rule
- Quotient Rule of Logarithms
- Solved examples of Log Rules
- Practise Questions on Log Rules