Help solving an equation

[rachaelmaria7]

Hello. I am working on an equation.

It is 4^x = 1
256

I think the answer is 1/64. I got that by dividing 256/4 which is 64. It this right or am I doing something wrong?

 

[pka]

How about if we know that
\(\displaystyle \L
\frac{1}{{256}} = 2^{ - 8}\)?

 

[Gene]

Something wrong.
It is 4^x so the best way is to use logs.
x*log(4)=log(1/256)
If you aren't comfortable with logs you can change it to powers of 2.
2^(2x)=2^(-8)
Now you have the bases equal so you can equate the exponents.

 

[rachaelmaria7]

I dt do too well with logs. But the answer wont be a fraction like I originally though. It islooking like -4 to me, but I could be wrong.

 

[Gene]

Nah, mathmaticians are never wrong. Ya done good!
Just be sure you understand what was done (and why) to get to powers of 2.