Final answer:
To find the solution of the exponential equation e³⁻⁵ˣ=16, take the natural logarithm of both sides and solve for x.
Step-by-step explanation:
To find the solution of the exponential equation e³⁻⁵ˣ=16, we need to isolate the variable x.
Step 1: Take the natural logarithm of both sides to cancel out the exponential function.
ln(e³⁻⁵ˣ) = ln(16)
Step 2: Simplify the equation using the property of logarithms that states ln(e) = 1.
(-5x)ln(e) = ln(16)
Step 3: Simplify further, since ln(e) = 1. Therefore, -5x = ln(16).
Step 4: Divide both sides by -5 to solve for x.
x = ln(16) / -5
Using a calculator to evaluate ln(16) / -5, we find that x ≈ -0.4781.