81 x−2 =27 2x

Sure, let's solve the equation step by step:

1. Rewrite the equation: 81x^(-2) = 27^(2x)
2. Take the natural logarithm (ln) on both sides: ln(81x^(-2)) = ln(27^(2x))
3. Use the properties of logarithms to simplify: -2ln(81x) = 2xln(27)
4. Divide both sides by 2: -ln(81x) = xln(27)
5. Rearrange the equation: xln(27) + ln(81x) = 0
6. Substitute u = ln(x): uln(27) + ln(81e^u) = 0
7. Solve for u using numerical methods (like Newton's method) or software tools.
8. Substitute back u = ln(x) to find the value of x.

Please note that this equation might not have a simple analytical solution and might require numerical methods or software tools to solve.