1. Instead of Fit Y by X use Fit Model. In the Fit Model dialog you can specify the Log transform for "y axis" and "x axis" using the "Transform" red triangle pull down.
2. In the output window use the red triangle pull down next to "Response Log(y axis)" and choose Save Columns > "Indiv Confidence Limit Formula". This places formulas for the upper and lower 95% CL for Individuals in the table.
3. In JMP using the menus choose Graph > Profiler.
4. In the Profiler select the lower CL formula for "Y, Prediction Formula" and click OK.
5. In the resulting window click the red triangle pull down next to "Prediction Profiler" and choose "Desirability Functions"
6. Alt click the Desirability Function and change it to "Match Target" and then set the middle value to be your target (0.6 in your example
7. Click the red triangle pull down next to "Prediction Profiler" and choose Maximize Desirability
In your example you should be able to see the result (0.0048582) on the horizontal axis label and the achieved target (0.6) on the vertical axis.