Solve for x: 131,072 = 2^x

Date: 09/12/2001 at 01:35:52
From: Niki Thiessen
Subject: Exponents

How do I solve the following equation for x:

131,072 = 2^x  

I know the answer is 17, but can't remember how to solve it.

Date: 09/12/2001 at 12:09:57
From: Doctor Peterson
Subject: Re: Exponents

Hi, Niki.

It depends on what tools you have. With a calculator (so I can handle 
logarithms), I would take the log of both sides and solve for x by 
dividing. By hand, I would just square 2 repeatedly until I got near 
131,072, and then find what additional doublings it takes:

   2^2 = 4
   2^4 = 4^2 = 16
   2^8 = 16^2 = 256
   2^16 = 256^2 = 65536

The next squaring would take me too far, so I divide 131072 by 65536 
and find that I just need to multiply by 2 one more time:

    131072 = 2 * 2^16 = 2^17

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/