Powers question

Sparks43

Right here goes

4^2=16

2^4=16


Can i simplify 256^4 down to 2^?

jeepers101

You can do this using logs.

logb(x)=a is another way of saying b^a=x

Example:

log2(16)=4 since 2^4=16

Now back to your problem. If you work out your problem 256^4 you will get some number, say x. You now need to find the log of x to the base 2, log2(x)

If you try and enter this into your calculator you might have some trouble due to the fact you cannot change the base.

Use this formula to get around it:



You can omit the 'k' when entering this into the calculator.

Yakuza

As 256 = 2^8. then (2^8)^4 = 2^(8*4) or 2^32.

Generally, (x^y)^z = x^(y*z).

Some more info here:http://www.mathsrev.com/rules-of-indices/

TheBody

You could think of the problem as trying to factor out all the 2's:

[latex]256^4=[2(128)]^4[/latex]
[latex]=[2(2)(64)]^4[/latex]
[latex]=[2(2)(2)(32)]^4[/latex]
[latex]=[2(2)(2)(2)(16)]^4[/latex]
[latex]=[2(2)(2)(2)(2)(8)]^4[/latex]
[latex]=[2(2)(2)(2)(2)(2)(4)]^4[/latex]
[latex]=[2(2)(2)(2)(2)(2)(2)(2)]^4[/latex]
[latex]=[2^8]^4[/latex]
[latex]=2^{32}[/latex]

Sparks43

Brilliant thanks

Doing a Network course and was trying to get combinations for sub netting and ipv4

So its nice to know that i was right and 2^32 is the same as 256^4 also it won me a few pints from so called experts