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

11 Answers

  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[2] to mean the log of base 2.

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

    log[2] 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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