Hello people. I wanted to know if it is possible to solve this problem.

I have a range : -$\displaystyle 2^{w-1}$ to $\displaystyle 2^{w-1}-1$

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- Sep 3rd 2010, 04:35 PMwidgagaGiven a base, find the exponent
Hello people. I wanted to know if it is possible to solve this problem.

I have a range : -$\displaystyle 2^{w-1}$ to $\displaystyle 2^{w-1}-1$ - Sep 4th 2010, 02:09 AMtonio
- Sep 4th 2010, 06:52 PMEducated
Widgaga has double posted his question, one with more detail than the other. The actual question is:

$\displaystyle Range = (2^{w-1}-1) - -2^{w-1}$

So if the range was 4 and you wanted to find w, then:

$\displaystyle 4 = 2^{w-1} -1 + 2^{w-1}$

$\displaystyle 4 = 2 * 2^{w-1}-1$

$\displaystyle 5 = 2 * 2^{w-1}$

$\displaystyle log{5} = log{2} + log{2^{w-1}}$

Can you continue using the law of logarithms to solve for w?