Final answer:
To rewrite the equation e^-2.5 = h in its logarithmic form, you take the natural logarithm of both sides to get ln(e^-2.5) = ln(h), which simplifies to ln(h) = -2.5, since the natural logarithm and the exponential function with base e are inverses of each other.
Step-by-step explanation:
The equation e^-2.5 = h can be rewritten as a logarithmic equation by using the properties of logarithms and exponentials, which are inverse functions of each other. This means that the natural logarithm function, often denoted as ln, can 'undo' the exponential function with base e. Therefore, to rewrite the given equation, we apply the natural logarithm to both sides.
When we take the natural logarithm of both sides, we get: ln(e^-2.5) = ln(h). Using the property that ln(e^x) = x, we can simplify the left side to -2.5. Thus, the equivalent logarithmic equation is: ln(h) = -2.5.
It's important to understand that the natural logarithm is essentially asking 'to what power must the base e be raised to get the given number?'. In this case, the base e should be raised to the power of -2.5 to get h. The base e is the mathematical constant approximately equal to 2.7182818, and it serves as the default base for the natural logarithm.