Question

How do you write $ \ln (13) $ in exponential form?

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
$
  x = {\log _y}a \\
  y = {a^x} \;
$
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 = 13 \\
  y = e \;
  $
Hence, the equation will become:
 $ \ln 13 = x $
As, we know that $ {\ln _e}e = 1 $ .
Therefore, the equation will become,
 $
  {\ln 13} = x \\
  {13} = {{e^x}} \\
  {{e^x}} = {13}
 $
Hence, $ \ln (13) $ in exponential form is $ {e^x} = 13 $ .
So, the correct answer is “ $ {e^x} = 13 $ ”.

Note: A logarithm is the power to which a number must be raised in order to get some other number. Example: $ {\log _a}b $ here, a is the base and b is the argument. Exponent is a symbol written above and to the right of a mathematical expression to indicate the operation of raising to a power. The symbol of the exponential symbol is $ e $ and has the value $ 2.17828 $ . Remember that $ \ln a $ and $ \log a $ are two different terms. In $ \ln a $ the base is e and in $ \log a $ the base is $ 10 $ . While rewriting an exponential equation in log form or a log equation in exponential form, it is helpful to remember that the base of exponent.