Question

How do you simplify $ \ln {e^4} $ ?

Answer 1

Hint: First we will convert this equation into the form $ {\log _a}b $ . Then we will evaluate all the required terms. Then we will apply the property. Here, we are using $ \log {a^b} = b\log a $ logarithmic property. The value of the logarithmic function $ \ln e $ is $ 1 $ .

Complete step-by-step answer:
We will first apply the logarithmic property to convert the equation to solvable form. Compare the given equation with formula and evaluate the values of the terms.
Here, the values are:
 $
  a = e \\
  b = 4 \;
  $
Hence, the equation will become:
 $ \ln {e^4} = 4\ln e $
As, we know that $ {\ln _e}e = 1 $ .
Therefore, the equation will become,
 $
  {\ln {e^4}} = {4\ln e} \\
  {\ln {e^4}} = {4 \times 1} \\
  {\ln {e^4}} = 4
 $
Hence, the simplified form of $ \ln {e^4} $ will be $ 4 $ .
So, the correct answer is “4”.

Note: Remember the logarithmic property precisely which is $ \log {a^b} = b\log a $ .
 While comparing the terms, be cautious. After the application of property when you get the final answer, tress back the problem and see if it returns the same values. Evaluate the base and the argument carefully. Also, remember that $ {\ln _e}e = 1 $ .