# How is that 2^n = 1024 becomes 1024 = 2^10?

Just as the question says. What is the procedure that they used to make 2^n = 1024 become 1024 = 2^10?

Thanks

1. This is simply approached by using logarithms (logs).

A log is the exponent that a number is raised to, to get the final answer.

In this case we have that 2^n=1024. If we take the log of both sides we see

Log(2^n)=log(1024). Using a law that comes with the logs, we bring the n out front,

nlog(2)=log(1024)

Then divide by log(2) on both sides. n=log(1024)/log(2).

If you try this out on a TI-83 or more calculator, you would see that the answer is 10.

*If you haven’t learned about logarithms, this may seem confusing, but this is the procedure to finding (n).

2. 2^n means: “How many times do you need to multiply 2 by itself to get the answer of 1024?”

If you are using a calculator, take logarithm of the base that matches the base in the problem. The base is the number raised to a power. So take the logarithm base 2 of both sides. I’ll use Log to mean the log of base 2.

Log (2^n) will simplify to just the power on the base, so you get just n.

log 1024 is 10 when you use the calculator.

If you are asked to work it out by hand, you would need to write out the powers of 2.

2 x 2 = 4 (2^2)

2 x 2 x 2 = 8 (2^3)

2 x 2 x 2 x 2 = 16 (2^4)

2 x 2 x 2 x 2 x 2 = 32 (2^5)

2 x 2 x 2 x 2 x 2 x 2 = 64 (2^6)

2 x 2 x 2 x 2 x 2 x 2 x 2 = 128 (2^7)

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 (2^8)

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512 (2^9)

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024 (2^10)

3. Ok David—

You could use logs to base 2 on this but you don’t have that on your calculator unless you use the change of base formula….a little cumbersome..

another way to think about this is this: you should know that 2^5 = 32 right.

So (2^5)^2 = 2^10 = 32^2 = 1024.

You could also do it by (2^2)^5 = 2^10 = 4^5 = 4^3*4^2= 64 * 16 = 1024.

4. 2^n = 1024

n log 2 = log 1024

n

= log 1024/log 2

= 10 log 2/ log2

= 10

2^10 = 1024

1024 = 2^10

5. I would do this. 1024/2 = 512, 512/2 = 256, 256/2 = 128, 128/2 = 64. But now 64 = 8 x 8 = 2x2x2 x 2x2x2 =2^6. So, now you have 1024 = 2 x 2 x 2 x 2 x 2^6 = 2^10.

6. 1024=2^10 so 2^n=2^10 since bases are equal so are the indices, n=10

What is the problem?

7. 2^n = 1024====> log is log_base 10

log 2^n = log 1024

n log 2 = log 1024 ===> from the rule of logs logx^m = mlogx

n = [log 1024] / [log 2]

n = 3.0103 / 0.30103

n=10

8. Its simple. All you need is a calculator. We are trying to find the exponent so the equation will be log_2 1024 is equal to n. Type in the first part of the equation into your scientific calculator and you should get your answer which is n is equal to 10.

9. https://shorturl.im/dSPh5

I’m running 800 mb of ram (with a AMD processor) and get the same – 768 mb. Some ram is used for the necessary functions, but I don’t think that much. Physically check how much is installed. If it’s not 1024, Contact the store or Acer.

10. When finding out the value of a power, use logarithms.

n = log_2(1024), where log_2 means log base 2, and 1024 is what you’re taking the log_2 of.

n = log_2(1024) = 10

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