Question

Find the inverse: y = 0.3ˣ
If you could explain the steps too that would be really helpful! :)

Answer 1

To find the inverse of the function y = 0.3ˣ, interchange x and y, take the logarithm of both sides, and solve for y.

Step-by-step explanation:

To find the inverse of the function y = 0.3ˣ, we need to interchange x and y and solve for y. The inverse function will be denoted as x = f⁻¹(y).

1. Start with the original equation y = 0.3ˣ.

2. Interchange x and y to get x = 0.3ʸ.

3. Solve for y by taking the logarithm of both sides: log(x) = ʸlog(0.3).

4. Divide both sides by log(0.3) to isolate y: ʸ = log(x) / log(0.3).

Therefore, the inverse function of y = 0.3ˣ is x = log(y) / log(0.3).