Need Help with (2^n) = 210? Get Expert Review Math Assistance Now!

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Homework Help Overview

The problem involves solving the equation (2^1)(2^2)(2^3)(2^4)...(2^n) = 210, where participants are trying to determine the value of n. The context is rooted in exponential functions and sequences.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the transformation of the product into a sum of exponents, questioning the implications of the arithmetic sequence and the nature of the resulting value. Some express confusion over the integer requirement for n and the implications of 210 not being a multiple of 2.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on the problem setup and the implications of their calculations. There is recognition of the need for n to be an integer, and some participants are exploring the consequences of their approaches.

Contextual Notes

Participants note that the problem may not yield an integer solution due to the properties of the number 210, which is not a multiple of 2. There is also mention of confusion regarding the correct formulas to apply in this context.

rocketboy
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Hey everyone, I am stuck on this question:
[tex](2^1)(2^2)(2^3)(2^4)...(2^n) = 210[/tex]

What is the value of n?

I'd love to post what I have so far, except that the problem doesn't involve much work, so as soon as I have the first step I'll have the last...and I haven't yet gotten the first (correct) step.

THANKS!
 
Last edited:
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[tex]2^{1+2+3+...+n}[/tex]=210
 
don't i feel stupid... :smile:

I was doing the exact same thing only with the tn = a + (n-1)d formula instead of the Sn = n/2[2a + (n-1)d] formula!

Thank you!
 
Last edited:
i found an answer which is not an integer!
 
Leong said:
i found an answer which is not an integer!

Since 210 is not a multiple of 2, that's to be expected.
 
it is contrary to the method, because 1 + 2+ 3 +.. +n indicates that n must be an integer if want to use the arithmetic sequence formulae.
 

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