Solve the following equation:𝑒−3ln(𝑥)=1125

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

1. First, we rewrite the equation to isolate the natural logarithm. The equation is e^(-3ln(x)) = 1125.

2. We know that e^(ln(x)) = x, so we can simplify the left side of the equation to x^(-3) = 1125.

3. To isolate x, we take the cube root of both sides. The cube root of x^(-3) is x^(-1), and the cube root of 1125 is 10.5. So, x^(-1) = 10.5.

4. Finally, to solve for x, we take the reciprocal of both sides. The reciprocal of x^(-1) is x, and the reciprocal of 10.5 is approximately 0.0952.

So, the solution to the equation e^(-3ln(x)) = 1125 is x ≈ 0.0952.