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If 3^(2x) = 81, what is the value of x?
If 3^(2x) = 81, what is the value of x?
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Q1
If 3^(2x) = 81, what is the value of x?
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Since 81 = 3^4, we have 3^(2x) = 3^4, thus 2x = 4, giving x = 2.
Questions & Step-by-step Solutions
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Q: If 3^(2x) = 81, what is the value of x?
Solution:
Since 81 = 3^4, we have 3^(2x) = 3^4, thus 2x = 4, giving x = 2.
Steps: 6
Show Steps
Step 1: Start with the equation 3^(2x) = 81.
Step 2: Recognize that 81 can be written as a power of 3. Specifically, 81 = 3^4.
Step 3: Rewrite the equation using this information: 3^(2x) = 3^4.
Step 4: Since the bases (3) are the same, we can set the exponents equal to each other: 2x = 4.
Step 5: Solve for x by dividing both sides of the equation by 2: x = 4 / 2.
Step 6: Simplify the right side: x = 2.
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