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 = 2³ and 4 = 2²

Now you have to write the equation as: 1/√2³ = 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.

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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..