# Finding a exponent

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 dont 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

HallsofIvy
Homework Helper
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.