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If 4^(x-1) = 64, what is the value of x?
If 4^(x-1) = 64, what is the value of x?
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Q1
If 4^(x-1) = 64, what is the value of x?
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Since 64 can be expressed as 4^3, we have 4^(x-1) = 4^3, thus x - 1 = 3, leading to x = 4.
Questions & Step-by-step Solutions
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Q
Q: If 4^(x-1) = 64, what is the value of x?
Solution:
Since 64 can be expressed as 4^3, we have 4^(x-1) = 4^3, thus x - 1 = 3, leading to x = 4.
Steps: 6
Show Steps
Step 1: Start with the equation 4^(x-1) = 64.
Step 2: Recognize that 64 can be rewritten as a power of 4. Specifically, 64 = 4^3.
Step 3: Now rewrite the equation using this information: 4^(x-1) = 4^3.
Step 4: Since the bases (4) are the same, we can set the exponents equal to each other: x - 1 = 3.
Step 5: Solve for x by adding 1 to both sides of the equation: x = 3 + 1.
Step 6: Therefore, x = 4.
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