In the ICSE Class 9 Mathematics syllabus, the topic of logarithms is introduced to students. Logarithms are a way to express numbers in a compact form, particularly useful for dealing with very large or very small numbers. Here’s a summary of the key concepts covered in this topic:

1. **Introduction to Logarithms**: Logarithms are the inverse functions of exponential functions. If ( a^b = c ), then ( log_a(c) = b ), where ( a ) is the base, ( b ) is the exponent, and ( c ) is the result.

2. **Basic Properties of Logarithms**:

– ( log_a(xy) = log_a(x) + log_a(y) )

– ( log_aleft(frac{x}{y}right) = log_a(x) – log_a(y) )

– ( log_a(x^n) = n cdot log_a(x) )

3. **Common Logarithms**: Logarithms with base 10 are called common logarithms. They are usually written as ( log(x) ) without specifying the base.

4. **Natural Logarithms**: Logarithms with base ( e ) (Euler’s number, approximately equal to 2.71828) are called natural logarithms. They are denoted by ( ln(x) ).

5. **Change of Base Formula**: ( log_a(b) = frac{log_c(b)}{log_c(a)} ), where ( c ) is any positive number different from 1.

6. **Applications of Logarithms**:

– Simplifying calculations involving large numbers or powers.

– Solving exponential equations.

– Understanding growth and decay in various real-world scenarios.

7. **Graphs of Logarithmic Functions**: The graph of a logarithmic function is a curve that approaches the x-axis but never touches it, with the curve getting closer to the x-axis as x approaches infinity.

This summary provides a basic overview of the logarithms topic covered in ICSE Class 9 Mathematics. It’s important for students to practice solving problems and applying logarithmic concepts to various situations to gain a deeper understanding of the topic.