1. What is Logarithm?

A logarithm is the inverse operation to exponentiation, just as division is the inverse of multiplication. The logarithm of a number x with respect to base b is the exponent to which b must be raised to yield x.

2. How Does the Calculator Work?

The calculator uses the logarithm formula:

Where:

• \( x \) — The number (must be positive)
• \( b \) — The base (must be positive and not equal to 1)
• \( y \) — The result (exponent)

Explanation: The calculator computes the logarithm using the change of base formula: \(\log_b(x) = \frac{\ln(x)}{\ln(b)}\).

3. Importance of Logarithms

Details: Logarithms are used throughout science and engineering when quantities span large ranges. They're essential in mathematics, physics, chemistry, computer science, and many other fields.

4. Using the Calculator

Tips: Enter any positive number and any positive base (except 1). The calculator will determine what power you need to raise the base to get the number.

5. Frequently Asked Questions (FAQ)

Q1: What is the natural logarithm?
A: The natural logarithm (ln) is a logarithm with base e (Euler's number ≈ 2.71828).

Q2: What is the common logarithm?
A: The common logarithm (log) typically refers to base 10 logarithms.

Q3: Why can't the base be 1?
A: The function 1^x always equals 1, so it's not useful for logarithms and would lead to undefined results.

Q4: What are logarithm identities?
A: Important identities include: log(ab) = log(a) + log(b), log(a/b) = log(a) - log(b), and log(a^b) = b·log(a).

Q5: How are logarithms used in real life?
A: They're used in measuring earthquake intensity (Richter scale), sound intensity (decibels), pH scale, and in algorithms for efficient computation.