Question

How do you solve `1/ sqrt 8 = 4^(m – 2)`?

Answer 1

The answer is `m=1 1/4`

Explanation:

When solving exponential equations (or inequalities) first you have to find a suitable common base. In this case it would be `2` because `8=2^3` and `4=2^2`.

Now you have to write the equation using calculated base:

`1/sqrt(2^3)=2^(2*(m-2))`

Now you can use the property of powers which says that `root(n)(a)=a^(1/n)`

`1/2^(3/2)=2^(2m-4)`

Next property to use is: `1/(a^x)=a^(-x)`

`2^(-3/2)=2^(2m-4)`

Now since we have the equality of 2 powers with equal base we can write it as the equality of exponents:

`-3/2=2m-4`

`2m=4-3/2`

`2m=2 1/2`

`2m=5/2`

`m=5/4=1 1/4`