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If log2(x) + log2(8) = 7, what is the value of x?
If log2(x) + log2(8) = 7, what is the value of x?
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If log2(x) + log2(8) = 7, what is the value of x?
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log2(x) = 7 - log2(8) = 7 - 3 = 4, so x = 2^4 = 16.
Questions & Step-by-step Solutions
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Q: If log2(x) + log2(8) = 7, what is the value of x?
Solution:
log2(x) = 7 - log2(8) = 7 - 3 = 4, so x = 2^4 = 16.
Steps: 7
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Step 1: Start with the equation: log2(x) + log2(8) = 7.
Step 2: Recognize that log2(8) can be simplified. Since 8 is 2 raised to the power of 3, log2(8) = 3.
Step 3: Substitute log2(8) with 3 in the equation: log2(x) + 3 = 7.
Step 4: To isolate log2(x), subtract 3 from both sides: log2(x) = 7 - 3.
Step 5: Calculate the right side: log2(x) = 4.
Step 6: To find x, rewrite the equation in exponential form: x = 2^4.
Step 7: Calculate 2^4, which equals 16.
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