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

Solution:

Given, the equation is 1/√8 = 4(m+3)

When solving exponential equations, first we have to find a suitable common base.

Now, 8 = 2³ and 4 = 2²

The above equation becomes 1/√2³ = 2^{2(m + 3)}

Using the property of powers

\(\sqrt[n]{a}\) = a^1/n

Now, 1/2^3/2 = 2^{(2m + 6)}

Using the property, 1/a^x = a^-x

2^-3/2 = 2^{2m + 6}

Now, we have the equality of 2 powers with an equal base.

We can write it as the equality of exponents as

-3/2 = 2m + 6

Grouping of common terms,

2m = -3/2 - 6

Dividing by 2 on both sides,

m = -3/4 - 3

m = (-3 - 12)/4

m = -15/4

m = -3¾

Therefore, the solution to the equation is -3¾

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 -3¾