# What is the solution to equation 1 over the square root of 8 = 4^{(m - 3)}?

**Solution:**

Given 1 over the square root of 8 = 4^{(m - 3)}

When solving exponential equations (or inequalities) first you have to make the bases equal.

Here,it would be 2 because 8 = 2^{3} and 4 = 2^{2}

Now you have to write the equation as: 1/√2^{3 }= 2^{2(m - 3)}

We know the property of powers which says that

n^{th}√a = a^{1/n}

1/ (2^{3/2}) = 2^{2m - 6} [since 1/a^{x }= a^{-x}]

2^{-3/2}= 2^{2m - 6}

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

⇒ -3/2= 2m - 6

⇒ -3 = 4m -12

⇒ -3+12 = 4m

m = 9/4 = 2 ¼.

## What is the solution to equation 1 over the square root of 8 = 4^{(m - 3)}?

**Summary:**

The solution to equation 1 over the square root of 8 = 4^{(m - 3)} is 2 ¼..

Math worksheets and

visual curriculum

visual curriculum