Question

rewrite the following in exponential form: \\(\ln 7.389 = 2\\)

Explanation:

Step1: Recall the definition of natural logarithm

The natural logarithm $\ln(x)$ is defined as the logarithm with base $e$, so $\ln(x) = y$ is equivalent to $e^y = x$ by the definition of logarithms (where if $\log_b(a)=c$, then $b^c = a$ and here $b = e$).

Step2: Apply the definition to the given equation

Given $\ln(7.389)=2$, using the definition of natural logarithm (base $e$), we can rewrite it in exponential form by identifying $y = 2$ and $x = 7.389$ in the formula $e^y=x$. So we get $e^2 = 7.389$.

Answer:

$e^2 = 7.389$