For what value of b is the line y = 10x tangent to the curve y = e^bx at some point in the xy-plane?

1. 10/e

2. 10

3. 10e

4. e^10

5. e

The answer was 1.

I tried finding where the two eqns intersect.

I also tried taking the derivative of y = e^bx and setting that = 10

How should I approach this problem? I am finding it difficult to simplify 10/e when working backwords from the answer.

Thank you very much in advance.