Finding Exponent for \sqrt{128} = 2^m

  • Thread starter thomas49th
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In summary, to find m in the equation \sqrt{128} = 2^{m}, you can first square both sides to get 128 = 2^(2m). Since 128 = 2^7, we can then take the log base 2 of both sides to get m = 7/2. Alternatively, you can use the fact that \sqrt{x}= x^{\frac{1}{2}} and 128= 2^7 to directly determine that m = 7/2. The use of log functions is not expected at a GCSE level.
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Hi, I have the equation


[tex]\sqrt{128} = 2^{m}[/tex]

I know that m is [tex]\frac{7}{2}[/tex] as 2^7 = 128 from binary.
However, say the equation was

[tex]\sqrt{128} = 2^{m}[/tex]

how do I go about finding m. Can someone show me the technique

Thankyou
Tom
 
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  • #2
square both sides and use logs
 
  • #3
we don't use log function at GCSE level
 
  • #4
Well informally, after squaring both sides you have 128=2^(2m). But youve already identified that 128=2^7. So 7=2m

What youre doing is finding the log base 2 of both sides. Log base 2 of 128 = 7 because 2^7=128. Log base 2 of 2^(2m)=2m because 2^(2m)=well... 2^(2m)
 
  • #5
how do I use the log function on a calculator? You will need a calculator right?
 
  • #6
thomas49th I teach GCSE and you are not expected to know about logs. You are expected to either know that 2^7=128 or to be able to work out the value using what you do know. So if you know 2^3=8, then you multiply by 2 to get 2^4=16 and to keep going until you get 128
 
  • #7
thomas49th said:
Hi, I have the equation


[tex]\sqrt{128} = 2^{m}[/tex]

I know that m is [tex]\frac{7}{2}[/tex] as 2^7 = 128 from binary.
However, say the equation was

[tex]\sqrt{128} = 2^{m}[/tex]

how do I go about finding m. Can someone show me the technique

Thankyou
Tom
You should know that [itex]\sqrt{x}= x^{\frac{1}{2}}[/itex]
Since 128= 27, then [itex]\sqrt{128}= 2^{\frac{7}{2}}[/itex]
Your equation [itex]\sqrt{128}= 2^m[/itex] is equivalent to [itex]2^{\frac{7}{2}}= 2^m[/itex] and, then, since 2x is a one-to-one function, we must have m= 7/2.
 

What is an exponent?

An exponent is a number that indicates how many times a base number should be multiplied by itself. It is written as a superscript to the right of the base number.

What is a square root?

A square root is the number that, when multiplied by itself, results in the given number. It is represented by the √ symbol.

How do I find the exponent for a given square root?

To find the exponent for a square root, you can use the property that √(a^b) = a^(b/2). So for √128 = 2^m, we can rewrite it as 128 = (2^m)^2. Then we can solve for m by taking the square root of both sides, giving us m = 7.

Why is the exponent for √128 equal to 7?

The exponent for √128 is equal to 7 because 128 is equal to (2^7)^2. This means that 128 is the result of multiplying 2 by itself 7 times, and then multiplying that result by itself again.

What is the significance of finding the exponent for a square root?

Finding the exponent for a square root allows us to better understand the relationship between a number and its square root. It also helps us to simplify expressions and solve equations involving square roots.

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