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.