Please Solve 4^x = 256 also if you can please show your work so I can actually learn how to do it.

Question

anonymous · Answer

Do you know about logarithms?

sambam · Answer

Not really

anonymous · Answer

$$ 4^x = 4^4\ x=4$$

anonymous · Answer

That's just one way.  As it turns out, 256 is a power of 4.

anonymous · Answer

no need for logs

anonymous · Answer

LIke he said.

anonymous · Answer

I know she does not need logs, but if she knew about them that would be good.  Unless you are highly familiar with all the powers of a number, it's just a calculator game until you hit the right power.

majacw · Answer

WolframAlpha.com and Mathway are great (FREE) math sites. Good luck!

skullpatrol · Answer

What is on the left side of this equation: $$4^x = 256 $$and what is on the right side of the equation look very different correct?

luigi0210 · Answer

I prefer Luis's method over logs

skullpatrol · Answer

@sambam  Try to make the sides "look" as much as possible the same.

jhannybean · Answer

$$\large 4^x = 256 $$$$\large 256= 4^4$$$$\large 4^x = 4^4$$$$\large \cancel4^x = \cancel4^4$$$$\large x= 4$$ when you have teh same base, you can just eliminate them and evaluate the powers.

nincompoop · Answer

4^x = 256
Perform the prime factorization of the left hand side.
4^x = 2^(2 x):
2^(2 x) = 256
Perform the prime factorization of the right hand side.
256 = 2^8:
2^(2 x) = 2^8
Equate exponents.
Equate exponents of 2 on both sides:
2 x = 8
Solve the linear equation.
All equations give x = 4 as the solution:
Answer: |  
x = 4

anonymous · Answer

I agree Luigi, but if you are not aware of the powers of 4 in this case you could just be sitting there.  These ease of solution comes from this knowledge.  I thought the questioner might not be aware of the connection between 4 and 256.

anonymous · Answer

I get on board with nincompoop.  There's some math there and not so much luck.

nincompoop · Answer

This is why it is important to have a very strong grasp of the fundamentals.  One can always exploit solutions from the basics.

skullpatrol · Answer

Or just divide 256 by 4 :)

anonymous · Answer

Preach on nincompoop!  Maybe you have been misnamed?

anonymous · Answer

I believe sambam left the arena.  Just a bunch of math - o - philes here now.