SOLUTION: I haven't done a problem like this for several years and I don't remember how to solve it! It's driving me crazy! Here is the problem: 1024=2^n-1. Solve for n. I don't rememb

Algebra ->  Exponents -> SOLUTION: I haven't done a problem like this for several years and I don't remember how to solve it! It's driving me crazy! Here is the problem: 1024=2^n-1. Solve for n. I don't rememb      Log On


   

Question 161664: I haven't done a problem like this for several years and I don't remember how to solve it! It's driving me crazy! Here is the problem:
1024=2^n-1. Solve for n.
I don't remember how to bring the exponent (n-1) down so that I can solve for n.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
There are at least two ways to solve this

Method #1:

1024=2%5E%28n-1%29 Start with the given equation


2%5E10=2%5E%28n-1%29 Rewrite 1,024 as 2%5E10. This is possible since 2%5E10=1024


Since the bases are equal (they are both 2), this means that the exponents are equal. So


10=n-1 Set the exponents equal to one another.


10%2B1=n%2Bcross%28-1%2B1%29 Add 1 to both sides.


11=n Add.


So the answer is n=11



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Method #2

1024=2%5E%28n-1%29 Start with the given equation


log%2810%2C%281024%29%29=log%2810%2C%282%5E%28n-1%29%29%29 Take the log of both sides.


log%2810%2C%281024%29%29=%28n-1%29log%2810%2C%282%29%29 Rewrite the right side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


log%2810%2C%281024%29%29%2Flog%2810%2C%282%29%29=n-1 Divide both sides by log%2810%2C%282%29%29


10=n-1 Evaluate log%2810%2C%281024%29%29%2Flog%2810%2C%282%29%29 to get 10


10%2B1=n%2Bcross%28-1%2B1%29 Add 1 to both sides.


11=n Add.


So the answer is n=11