Math Problem Statement
Solution
The equation shown in the image is:
To solve for , we can rewrite both sides of the equation with the same base. Here’s the step-by-step solution:
Step 1: Rewrite as a power of 4
Since , we can write as:
So the equation becomes:
Step 2: Set the exponents equal to each other
Since the bases are the same, we can equate the exponents:
Step 3: Solve for
Subtract 1 from both sides:
Final Answer
Would you like further details or have any questions about the steps?
Here are five related questions to explore this topic further:
- What is an exponential equation, and how do we solve equations with different bases?
- How can we handle exponential equations where the bases cannot be easily matched?
- What is the meaning of a negative exponent, and why does ?
- How do we approach solving equations with logarithmic properties?
- How would the solution change if the base were different (e.g., )?
Tip: When solving exponential equations, always check if you can rewrite both sides with the same base—it often simplifies the problem significantly!
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Math Problem Analysis
Mathematical Concepts
Exponents
Algebra
Exponentials
Formulas
a^m = 1/a^(-m)
Exponential equation property: if a^m = a^n, then m = n
Theorems
Exponentiation rules
Properties of exponents with negative powers
Suitable Grade Level
Grades 9-11