X^0.281 = 7.72 How do I solve for X?

For both sides do the root of 0.281, thus giving you the answer.

When rooting the left side by 0.281, it will cancel out both and it will leave you with the 00.281 root of 7.72.

So it would be: X=(7.72)^(1/0.281)

Or X=0.281root of 7.72

You need tor root the second number by the power.

E.g. if it was x^2 - 25, x = root(25) = 5

So it's the 0.281th root of 7.72

You're more likely to see that written as 7.72^(1/0.281) though.

I would divide 7.72/0.281=27.4733096085 and to check it take the answer and time it time 0.281 I got 7.72 back when I rounded which make me think its right what you think

x^0.281 = 7.72 is the same as 0.281lgx = lg7.72

lgx = lg7.72/ 0.281

lgx = 3.158780428

x = 10^3.158780428

x = 1441.386426

x^0.281 = 7.72

take ln LN (Natural Logarithm) of both sides

LN(x^0.281) = LN 7.72

0.281 LN x = LN 7.72

LN x = (LN 7.72)/0.281 ≈ 7.27336

x ≈ e^(7.27336) ≈ 1441.386

x^(0.281) = 7.72

0.281 * ln(x) = ln(7.72)

ln(x) = ln(7.72) / 0.281

ln(x) = ln(7.72^(1/0.281))

x = 7.72^(1/0.281)