The function is defined by . If , then the value of must be:
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Got it in about 40 seconds. Just add 5 to both sides, then think powers of 2. 68 = 2^6 + 4, so x is definitely bigger than 7. Nice one.
Same approach here, but I almost picked C by rushing the comparison.
Wait, can someone explain why 68 isn't just rounded to 64? I set 2^(x-1) = 68 and then got stuck deciding between 7 and 8.
64 is 2^6 and 128 is 2^7, so x-1 has to be between 6 and 7. That means x is between 7 and 8.
Oh right, because the +5 is on the outside. Thanks!
This felt a bit tricky for a 600-level question because the answer choices are ranges, not exact values. Took me a second to trust the exponent comparison.
Nice question. I like that it tests estimation with powers of 2 instead of just solving directly. Bookmarking this one.
Agreed, good reminder that not every function question needs a clean integer answer.
What it tests
Your ability to evaluate and compose functions, including unusual defined operations.
Common trap
Applying function operations in the wrong order or ignoring domain restrictions.