5e^6x+3 = 0.1

How do I solve this?

-1.152 to the nearest thousandth.

Step-by-step explanation:

5e^6x+3 = 0.1

Divide both sides by 5:

e^6x+3 = 0.02

Take logs to the base e of both sides:

ln e^ (6x+3) = ln 0.02

6x + 3 = ln 0.02 (by the definition of a logarithm).

x = (ln 0.02 - 3) / 6

x = - 1.152.