Question #6444927Fill in the Blank
Algebra-1
Question
Solve the equation . The value of x is ________.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to solve exponential equations by rewriting both sides with the same base. The key is to recognize that both and can be expressed as powers of 4.
This question tests the student's ability to solve exponential equations by rewriting both sides with the same base. The key is to recognize that both and can be expressed as powers of 4.
Key Concept Explanation
The core principle is that if two exponential expressions with the same base are equal, their exponents must be equal. This is because the exponential function is injective (one-to-one).
The core principle is that if two exponential expressions with the same base are equal, their exponents must be equal. This is because the exponential function is injective (one-to-one).
Step-by-step Solution
1. Rewrite and as powers of 4: and .
2. Substitute these into the equation: .
3. Simplify the exponents:
1. Rewrite and as powers of 4: and .
2. Substitute these into the equation: .
3. Simplify the exponents:
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