Final answer:
To convert the exponential equation e^(x+1) = 0.5 to logarithmic form, take the natural logarithm of both sides, resulting in x+1 = ln(0.5), and then isolate x by subtracting 1 to get x = ln(0.5) - 1.
Step-by-step explanation:
To express the equation ex+1 = 0.5 in logarithmic form, we need to use the property of natural logarithms. The natural logarithm is the inverse of the exponential function when the base is e, the Euler's number (approximately 2.71828). To solve for x, we take the natural logarithm of both sides of the equation:
ln(ex+1) = ln(0.5)
Since the natural logarithm and the exponential function are inverses of each other, ln(ex+1) simplifies to x+1:
x+1 = ln(0.5)
To solve for x, subtract 1 from both sides:
x = ln(0.5) - 1
This equation is now in logarithmic form, representing the original exponential equation.