Exercise 1.4 Question 7 | Solve Exponential Equations for 'm' | Class 9 Math | Solve It With Shoaib

Exercise 1.4 Question 7 | Solve Exponential Equations for 'm' | Class 9 Math | Solve It With Shoaib

Welcome to Solve It With Shoaib! In our final video for Exercise 1.4, we tackle the challenging Question 7. This is a very important type of problem where you need to solve for a variable in the exponent.

The problem is to solve the following equation for "m":
36 to the power of (2m minus 5), all divided by 6 to the power of (3m minus 5), equals 216 to the power of (m plus 6).

This tutorial is designed to be clear and helpful for all students in Bhimber, Azad Kashmir, and across Pakistan preparing for their mathematics exams.

Key Concepts & Strategy Covered:
This question combines all your knowledge of exponents to solve what is called an exponential equation.

Exponential Equation: An equation where the variable we need to solve for (in this case, 'm') is located in the exponent.

The Golden Rule (Common Base): The key to solving most exponential equations is to rewrite every term in the equation so that they all have the same base number. For this problem, the common base for 36, 6, and 216 is 6.

Laws of Exponents: We will use the power rule (like 'a' to the power of 'm', all raised to the power of 'n', equals 'a' to the power of 'm times n') and the quotient rule (like 'a' to the power of 'm' divided by 'a' to the power of 'n' equals 'a' to the power of 'm minus n') to simplify the equation after finding the common base.

Equating Exponents: Once the equation is in the form "Base to the power of X equals Base to the power of Y" (where Base is the common base), we can simply set the exponents equal to each other (X equals Y) and solve the resulting algebraic equation.

In the video, we'll walk through each of these steps: converting to base 6, simplifying using exponent laws, and solving for 'm'.

With this video, you have completed Exercise 1.4! We hope this series has been helpful. Please LIKE and SHARE if you learned something, and SUBSCRIBE to Solve It With Shoaib for more math tutorials. Leave a COMMENT with your questions or to let us know which exercise you want to see next!

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