221k views
4 votes
Find the inverse: y = 0.3ˣ
If you could explain the steps too that would be really helpful! :)

User Krishg
by
7.3k points

1 Answer

7 votes

Final answer:

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).

User Torian
by
8.1k points

Related questions

asked Nov 12, 2024 26.2k views
Lucas Lazaro asked Nov 12, 2024
by Lucas Lazaro
7.9k points
1 answer
1 vote
26.2k views
asked May 14, 2024 5.5k views
Sergei Volkov asked May 14, 2024
by Sergei Volkov
8.3k points
1 answer
2 votes
5.5k views
asked Jul 21, 2024 211k views
Amit Karsale asked Jul 21, 2024
by Amit Karsale
8.5k points
1 answer
1 vote
211k views