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The solution to the equation [tex]e^x = 198[/tex] is the exponent on [tex]e[/tex] needed to produce a value of 198. We can represent the solution in logarithmic form as [tex]\log_e (198)[/tex] or as:

[tex]x = \ln(198)[/tex]

Answer :

The solution to the equation ex = 198 can be expressed as ln(198). The natural logarithm ln is used as it is the inverse process of taking e to the power of x; hence x equals the natural logarithm of 198.

The solution to the equation ex = 198 can indeed be represented in logarithmic form, which allows us to find the exponent on e (Euler's number, approximately 2.71828) needed to produce a value of 198. The logarithmic form of this equation is expressed as ln(198), where ln stands for the natural logarithm, that is, the logarithm to the base e.

To solve for x, we use the natural logarithm because it is specifically designed to deal with situations where the base is e. Thus, if we take the natural log of both sides of the equation, we get

ln(ex) = ln(198).

By the properties of logarithms, ln(ex) simplifies to x, because the natural logarithm of e to any power is just that power. So, the solution to our equation is x = ln(198), which we can calculate to find the precise value.

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