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Solve the following exponential equations : 3 power 4x = 1 upon 81
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Solve the following exponential equations : 3 power 4x = 1 upon ...
Understanding the Equation
To solve the equation \(3^{4x} = \frac{1}{81}\), we first need to express both sides of the equation with the same base.
Rewriting the Right Side
- Note that \(81\) can be rewritten as a power of \(3\):
- \(81 = 3^4\)
- Hence, \(\frac{1}{81}\) can be expressed as:
- \(\frac{1}{81} = 3^{-4}\)
Now, we can rewrite the equation:
Transforming the Equation
- The original equation \(3^{4x} = \frac{1}{81}\) becomes:
- \(3^{4x} = 3^{-4}\)
Setting the Exponents Equal
Since the bases are the same, we can set the exponents equal to each other:
- \(4x = -4\)
Solving for x
To find \(x\), divide both sides by \(4\):
- \(x = \frac{-4}{4}\)
- \(x = -1\)
Final Answer
The solution to the equation \(3^{4x} = \frac{1}{81}\) is:
- \(x = -1\)
This method illustrates the importance of expressing exponential equations with the same base, allowing for straightforward comparison of exponents.
To solve the equation \(3^{4x} = \frac{1}{81}\), we first need to express both sides of the equation with the same base.
Rewriting the Right Side
- Note that \(81\) can be rewritten as a power of \(3\):
- \(81 = 3^4\)
- Hence, \(\frac{1}{81}\) can be expressed as:
- \(\frac{1}{81} = 3^{-4}\)
Now, we can rewrite the equation:
Transforming the Equation
- The original equation \(3^{4x} = \frac{1}{81}\) becomes:
- \(3^{4x} = 3^{-4}\)
Setting the Exponents Equal
Since the bases are the same, we can set the exponents equal to each other:
- \(4x = -4\)
Solving for x
To find \(x\), divide both sides by \(4\):
- \(x = \frac{-4}{4}\)
- \(x = -1\)
Final Answer
The solution to the equation \(3^{4x} = \frac{1}{81}\) is:
- \(x = -1\)
This method illustrates the importance of expressing exponential equations with the same base, allowing for straightforward comparison of exponents.
Community Answer
Solve the following exponential equations : 3 power 4x = 1 upon ...
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Solve the following exponential equations : 3 power 4x = 1 upon 81
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Solve the following exponential equations : 3 power 4x = 1 upon 81 for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Solve the following exponential equations : 3 power 4x = 1 upon 81 covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following exponential equations : 3 power 4x = 1 upon 81.
Solve the following exponential equations : 3 power 4x = 1 upon 81 for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Solve the following exponential equations : 3 power 4x = 1 upon 81 covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following exponential equations : 3 power 4x = 1 upon 81.
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