Solving Exponent Equations: 6 to the Power of -2x Equals -36

Exponent equations can be tricky, but with a little practice, you can master them! Let's dive into solving an example: 6 to the power of -2x equals -36.

Understanding the Problem

The equation we are working with is: 6^-2x = -36

Our goal is to isolate the variable 'x'. To do that, we need to use the properties of exponents and logarithms.

Steps to Solve

1. Recognize the Problem: Notice that we cannot directly equate the bases (6 and -36). This means we need a different approach.
2. Rewrite the Equation: Since -36 is a negative number, we cannot express it as a power of 6. This means there is no solution to this equation. We can't find a value for 'x' that satisfies the equation.

Why No Solution?

Exponents involving a positive base, like 6, will always result in a positive output. There is no way to raise 6 to any power and get a negative result like -36.

Key Takeaways

• Exponents with positive bases always result in positive outputs.
• When solving exponent equations, always check if the equation is solvable based on the properties of exponents.

Practice Makes Perfect!

Try solving other exponent equations using the same principles. Remember to analyze the equation carefully and use the properties of exponents to find a solution.

If you encounter difficulties, don't hesitate to ask your teacher or consult online resources for further guidance.