Introduction to Logarithms:
Logarithms are mathematical functions that represent the exponent to which a base must be raised to produce a given number. They are widely used in various fields such as mathematics, physics, engineering, and economics.

Understanding Logarithmic Functions:
- Logarithmic functions are the inverse of exponential functions.
- The logarithm of a number x to the base b is denoted as log_b(x).
- Logarithms help in simplifying complex calculations involving exponents.

Properties of Logarithms:
- Product Rule: log_b(xy) = log_b(x) + log_b(y)
- Quotient Rule: log_b(x/y) = log_b(x) - log_b(y)
- Power Rule: log_b(x^a) = a*log_b(x)
- Change of Base Formula: log_a(x) = log_b(x) / log_b(a)

Applications of Logarithms:
- Logarithms are used in solving exponential equations.
- They are used in calculating compound interest, pH levels, and earthquake magnitudes.
- Logarithmic scales are used in measuring sound intensity (decibels) and earthquake intensity (Richter scale).

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