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

• thomas49th
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.

#### thomas49th

Hi, I have the equation

$$\sqrt{128} = 2^{m}$$

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

$$\sqrt{128} = 2^{m}$$

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

Thankyou
Tom

square both sides and use logs

we don't use log function at GCSE level

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)

how do I use the log function on a calculator? You will need a calculator right?

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

thomas49th said:
Hi, I have the equation

$$\sqrt{128} = 2^{m}$$

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

$$\sqrt{128} = 2^{m}$$

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

Thankyou
Tom
You should know that $\sqrt{x}= x^{\frac{1}{2}}$
Since 128= 27, then $\sqrt{128}= 2^{\frac{7}{2}}$
Your equation $\sqrt{128}= 2^m$ is equivalent to $2^{\frac{7}{2}}= 2^m$ 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.