To solve the expression (0.008924 ÷ 0.06731)^2 using logarithm methods, you can follow these steps:

1. Take the square of the entire expression: (0.008924 ÷ 0.06731)^2 = 0.008924^2 ÷ 0.06731^2
2. Now, we can use logarithms. Take the logarithm (base 10) of both sides of the equation:
   log((0.008924^2 ÷ 0.06731^2)) = log(0.008924^2) - log(0.06731^2)
3. Apply the power rule of logarithms to bring down the exponents as multipliers:
   log((0.008924^2 ÷ 0.06731^2)) = 2 * log(0.008924) - 2 * log(0.06731)
4. Calculate the logarithms:
   log((0.008924^2 ÷ 0.06731^2)) = 2 * (-2.04904) - 2 * (-1.17286)
5. Now, multiply the values:
   log((0.008924^2 ÷ 0.06731^2)) ≈ -4.09808 + 2.34572
6. Add the values:
   log((0.008924^2 ÷ 0.06731^2)) ≈ -1.75236
7. To find the original expression, take the antilog (base 10) of both sides:
   0.008924^2 ÷ 0.06731^2 ≈ 10^(-1.75236)
8. Calculate the right side:
   0.000079746 ÷ 0.00438469 ≈ 0.0179606

So, (0.008924 ÷ 0.06731)^2 ≈ 0.0179606 when solved using logarithm methods.