How to determine 2^x = 64

Question

I know the answer to this question is 6... but I am wondering what the formula is to figure this out.

I will always need to solve for x in this scenario.

TIA

you question doesn't belong here. post it at http://math.stackexchange.com — Nagri, Oct 12 '12 at 04:22

score 3 · Answer 1 · answered Oct 12 '12 at 04:22

3

Simply what you have to do is take the logarithm (base 2) of the right hand side. Like

log2(64) = 6

I think you should read a mathematics book which has topics related to logarithms.

answered Oct 12 '12 at 04:22

xeon111

score 2 · Accepted Answer · answered Oct 12 '12 at 04:22

2

log(64) / log(2) = x. Or in more general terms, if y^x = z, then x = log(z) / log(y)

answered Oct 12 '12 at 04:22

nithins

This works, but using the natural log is a bit roundabout. – cheeken Oct 12 '12 at 04:24

score 1 · Answer 3 · answered Oct 12 '12 at 04:22

1

Divide 64 by 2 continuously till you get 1 as result. The number of times you can divide is the answer.

ie

64/2 = 32  --- 1
32/2 = 16  --- 2
16/2 = 8   --- 3
8/2  = 4   --- 4
4/2  = 2   --- 5
2/2  = 1   --- 6

It stops here since you got answer 1. Now you have done it 6 times, hence 6 is the answer

answered Oct 12 '12 at 04:22

Sree

-1: only works for integer x. What if 2^x = 65? – Rody Oldenhuis Oct 12 '12 at 08:20

score 1 · Answer 4 · answered Oct 12 '12 at 04:23

1

a^b=y
=> ln(a)*b=ln(y)
=> b=ln(y)/ln(a)

answered Oct 12 '12 at 04:23

Adriaan Stander

score 0 · Answer 5 · answered Oct 12 '12 at 04:24

0

Here it is step by step, although some steps may seem not obvious if you don't understand logarithms.

2 ^ x = 64

log (2 ^ x) = log 64

x log 2 = log 64

x = log 64 / log 2

x = 6

answered Oct 12 '12 at 04:24

Trott

5 Answers5