Question

write the following equation as an equivalent exponential equation.
ln(11) = x

the equation ln(11) = x is equivalent to the exponential equation \square.

Explanation:

Step1: Recall the definition of natural logarithm

The natural logarithm $\ln(y)$ is defined as the exponent to which the base $e$ must be raised to obtain $y$. In other words, if $\ln(y)=x$, then by the definition of the natural logarithm, we can rewrite this in exponential form using the base $e$. The relationship between the logarithmic form $\ln(y) = x$ and the exponential form is given by the formula: if $\ln(y)=x$, then $e^{x}=y$.

Step2: Apply the definition to the given equation

In the given equation $\ln(11)=x$, we identify $y = 11$ and $x$ as the exponent. Using the formula from Step 1, we substitute $y = 11$ and the given $x$ into the exponential form. So, replacing $y$ with $11$ and the left - hand side's $x$ (from $\ln(11)=x$) into $e^{x}=y$, we get $e^{x}=11$.

Answer:

$e^{x}=11$