How do i calculate the power x

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In summary: So why bother with logs to start with?In summary, to find the value of x in the equation 2^x=128, you can either take the log of both sides and solve for x, or you can find the prime factorization of 128 and count the factors of 2 to determine the exponent. Both methods will yield the same answer of x=7.
  • #1
chemart
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[tex]2^x=128[/tex]
[tex]x=?[/tex]

how do i calculate power x from 128 and 2?
 
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  • #2
chemart said:
[tex]2^x=128[/tex]
[tex]x=?[/tex]

how do i calculate power x from 128 and 2?

You take the log of both sides:

log(2^X)=log(128)
Then you use the property
that log(a^b)=b log(a)

The remaining steps should be apparent.
 
  • #3
Or quicker, just calculate 2*2*2... until you get 128!
 
  • #4
mgb_phys said:
Or quicker, just calculate 2*2*2... until you get 128!

that's not quicker...
 
  • #5
ice109 said:
that's not quicker...

Depends how far away your calculator is.
 
  • #6
chemart said:
[tex]2^x=128[/tex]
[tex]x=?[/tex]

how do i calculate power x from 128 and 2?

2x = 128

the first thing you have to do is get both of the bases the same so in 2x, x is the exponent (or power if you like) and 2 is the base. So what you have to do is get 128 with a base of 2. So,

128 = 2 * 2 * 2 * 2 * 2 * 2 * 2

128 = 27

There for,

2x = 27

So,

x = 7

This way may seem long, but take the example of 22(x+1) = 1024

1024 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
= 210


22(x+1) = 210

2(x+1) = 10

2x + 2 = 10

2x = 8

x = 4
 
  • #7
there are also other cases where you have to take logs of both parts, like it initially was suggested. Say you have:

[tex]2^{x+1}=35[/tex] you defenitely cannot express 35 as a power of 2, so in these cases you need to take the log of both parts, and choose a base that will be easier to work with.
[tex]log_a 2^{x+1}=log35=>(x+1)log_a 2=log_a35=>x+1=\frac{log_a35}{log_a2}[/tex]
 
  • #8
ice109 said:
that's not quicker...

Yes it is -
1, you can do it in your head in the time it takes to find the log button on the calculator

or if you happen to be an android
2, multiplying by 2 is a single shift instruction in a register which you can do in a single clock cycle, it would take at least 7 clock cycles to load the instruction into the FPU and get the answer back - especially if you have a long pipeline.
 
  • #9
Too Simple! find the prime factorization of 128. Now, what is the exponent?

128 = 2 * 64 = 2 * 2*2*2 * 2*2*2

Count the factors of 2 in the factorization of 128.
 
  • #10
mgb_phys way is definitely quicker. Note when we take logs of both sides, all we achieve is [itex]x= log_2 (128)[/itex], and to actually evaluate that we must work out [itex]2^7 = 128[/itex] anyway.
 

1. How do I calculate the power of a number?

To calculate the power of a number, you need to use the exponent operator (^) in a mathematical equation. The base number is raised to the power of the exponent to get the final result. For example, to calculate 2 to the power of 3, the equation would be 2^3, which equals 8.

2. What is the difference between power and exponent?

Power and exponent are often used interchangeably, but they have different meanings in mathematics. Exponent refers to the number that indicates how many times a base number is multiplied by itself. Power, on the other hand, is the result of raising a base number to an exponent. In the equation 2^3, 2 is the base number and 3 is the exponent, while 8 is the power.

3. How do I calculate the power of a negative number?

Calculating the power of a negative number follows the same rules as a positive number. The only difference is that the base number is multiplied by itself the number of times indicated by the exponent. For example, to calculate (-2)^3, the equation would be (-2) x (-2) x (-2), which equals -8.

4. What is the power of zero?

The power of zero is always equal to 1. This is because any number raised to the power of 0 is equal to 1. For example, 5^0 equals 1, 10^0 equals 1, and so on.

5. Can I calculate the power of a decimal or fraction?

Yes, you can calculate the power of a decimal or fraction by following the same rules as with whole numbers. For example, to calculate 1.5^2, the equation would be 1.5 x 1.5, which equals 2.25. Similarly, to calculate 2^(1/2), the equation would be the square root of 2, which equals approximately 1.41.

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