Question 242094
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Well, the back of the book missed it by <b><i>that</i></b> much.


If *[tex \Large x\ =\ 4], then *[tex \Large x\ +\ 1\ =\ 5], and *[tex \Large 5^3\ =\ 125].  But *[tex \Large 2^7\ =\ 128].  That tells us that *[tex \Large x] has to be a little bit bigger than 4, i.e. precisely the cube root of 128 minus 1.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2^7\ =\ (x\ +\ 1)^3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ 1\ =\ \sqrt[3]{128}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 4\sqrt[3]{2}\ -\ 1\ \approx\ 4.04]


Now, if perchance your text book gave you instructions to round to the nearest whole number, then 4 is, in fact, the correct answer. You might also want to re-check the answer in the back to make sure the decimal part of the answer didn't wrap to the next line.  Barring any of that, write letters to the publisher and the author suggesting that they hire a proofreader next time they get it into their head to publish a textbook.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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