\(31 = 2^x - 3\)
\(2^x = 34\)
\(x = \log_2 (34) \)

Don't worry, no knowledge of logarithms is needed. The key is to see that \(2^5 = 32\) and \(2^6 = 64\). Hence the answer is between 2 and 5.

Given that \(f(x)=2^x-3\) and f(x)=31, and we need to find the range in which x lies

\(f(x)=2^x-3\) = 31
=> \(2^x\) = 31+ 3 = 34

Now, we know that \(2^5\) = 32 and \(2^6\) = 64
So, x will be between 5 and 6

So, Answer will be E
Hope it helps!

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