Solve e^x = 7.

• A. x = e^7
• B. x = 7e
• C. x = log_7 e
• D. x = ln(7)

Answer: (D)

Exponential and logarithmic functions are inverse processes, so to solve e^x = 7 you use a natural log. Take the natural log of both sides: ln(e^x) = ln 7. Since ln(e^x) = x, you get x = ln 7. This value is the power you must raise e to in order to obtain 7.

The other forms don’t solve for the exponent in e^x. For example, x = e^7 would mean something different (it says x is the result of raising e to 7), and x = 7e mixes an exponential with a linear product. log base 7 of e asks for the exponent needed to get e from 7, not the exponent in e^x = 7. So the correct expression is the natural logarithm of 7.