Final answer:
To solve the exponential equation -3e^9x - 1 + 6 = -58, one must isolate the e^9x term, take the natural logarithm, and solve for x. The solution, rounded to four decimal places, is approximately x = 0.2367.
Step-by-step explanation:
The equation provided is -3e9x - 1 + 6 = -58. Let's solve this equation step by step:
Add 1 to both sides of the equation to isolate the exponential term: -3e9x = -58 + 1.
Simplify the right side of the equation: -3e9x = -57.
Divide both sides by -3 to solve for e9x: e9x = 19.
Take the natural logarithm of both sides to remove the exponent: ln(e9x) = ln(19).
Simplify using the property of logarithms that ln(ex) = x: 9x = ln(19).
Divide by 9 to solve for x: x = ln(19) / 9.
Use a calculator to find the decimal approximation: x ≈ 0.2367 (rounded to four decimal places).
So, the solution to the equation is approximately x = 0.2367.