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The solution to the equation in logarithmic form is \(\log_e(198)\), or as:

198 is the exponent on \(e\) needed to produce a value of 198. How can we represent the solution?

Answer :

The natural logarithm of a number, denoted as ln, is the exponent to which e must be raised to produce that number. Thus, the solution to find the power needed on e to get 198 is written as ln(198).

The solution to the given equation involves the concept of logarithms, particularly those with base e. The natural logarithm of a number is the power to which e must be raised to equal that number. The constant e is approximately equal to 2.7182818. For instance, if we want to express the natural logarithm of 198, we are seeking the exponent that e must be raised to in order to get the value of 198.

To write the solution in logarithmic form, we say ln(198), which is read as 'the natural log of 198.' If we were to use a calculator to find this value, it would give us the specific exponent that when e is raised to it, it produces 198. Natural logarithms and exponential functions are inverse operations, meaning one undoes the other. Therefore, this is why the natural logarithm of the number e itself is simply 1.

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