Entrance Exam For Harvard University ( Math Question )

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I literally solved this mentally in 5 seconds lol

rajeshsoundararajan

Bro, 68 is the same as 64 + 4 which is 2^6 + 2^2
if 2^3x + 2^x = 2^6 + 2^2
then x is 2 for sure duh

jordisimon

Wouldn't it be faster to use trial and error? It's pretty clear that 2 is he answer

vinyasbharadwaj

2 is an obvious solution. 8^x is always increasing and greater than zero, the same applies for 2^x, therefore 2 is the only real solution

romanvolotov

solved in 10 seconds without any roots

srenTree

The comments saying you can do it mentally. Yes obviously you can but it's not about having the right answer as fast as possible. The whole point of this is to make a reproduceable method to arrive at the correct answer. Other similar questions to this will not be possible to do through mental math and trial and error. You learn the sure method to always be able to solve these problems.

hotman

It factors into 2^x(2^2x+1) = 68 = 4*17, so 2^x=4, x=2

irajasivadas

... A good day to you, This was a clear presentation from a to z; I also thought of this exercise in a graphical way: f(x) + g(x) = 68, so adding two exponential functions' y values up to 68, which can only be achieved with x = 2 in a Real sense, according to your calculations ... possibly a question could be: What are the answers of 2^x = - 2 +/- SQRT(13) * i, and what do they mean? Thank you for your continuing math efforts, Jan-W

jan-willemreens

i thought doing the binary decomposition, where 68 can be expressed as 1000100, which means 68 can be written like the sum of 1x2^2 + 1x2^6, so x must be 2.

Alvareque