# Proofs and Rules of Logarithms

## What are the proofs or rules of logarithms?

The proofs are statements that are used to validate or invalidate a logarithmic expression.

There are several proofs of logarithms; some of them are:

- Product rule
- Quotient rule
- Power rule
- Change of base

The common property in the first three proofs (listed above) is:

log_b(b^y) = y

This is so because, it links all the three proofs.

**Answer:**

The Answer is D

**Explanation:**

Is correct on edge

When proving the product, quotient, or power rule of logarithms, various properties of logarithms and exponents must be used. The property that must be used in all the proofs is: log_b(b^y) = y

Logarithms have specific rules and proofs that help in solving complex mathematical expressions involving exponents. The product rule states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the individual numbers. The quotient rule states that the logarithm of the quotient of two numbers is equal to the difference of the logarithms of the individual numbers. The power rule, on the other hand, states that the logarithm of a number raised to a power is equal to the product of the power and the logarithm of the number.

These rules are essential in simplifying logarithmic expressions and solving equations involving logarithms. By understanding and applying these rules, mathematicians and students can efficiently work with logarithmic functions and expressions.