Question

Write the equation in its exponential form.

A) x = e^2
B) x = 2^e
C) x = \ln(2)
D) x = e^{(e^2)}

Answer 1

To write 'x = \ln(2)' in its exponential form, we use the inverse relationship between the natural logarithm and the exponential function. Therefore, 'e^x = 2' is the exponential form of 'x = \ln(2)'.

Step-by-step explanation:

Converting equations to their exponential form often involves using the properties of logarithms and the number e, where e represents Euler's number, approximately equal to 2.7182818.

For part C of your question, 'x = \ln(2)', we'll apply the fact that the natural logarithm function and the exponential function are inverses of each other. The equation 'x = \ln(2)' can be rewritten in its exponential form by recognizing that the natural logarithm, \ln, represents the power to which e has to be raised to yield the number. Therefore, if 'x = \ln(2)', then 'e^x = 2'. In other words, 2 is e raised to the power of x.

We can generalize this trick for any base number b, where 'b = \ln(b)' can be rewritten as 'e^x = b', and for our specific case, 'e^x = 2' is the exponential form of 'x = \ln(2)'.