Question

question 8 of 10
which of the following exponential equations is equivalent to the logarithmic
equation below?
ln x = 7

a. x = e^7
b. x = \frac{7}{e}
c. x = 7e
d. x = 7e

Explanation:

Step1: Recall the definition of natural logarithm

The natural logarithm $\ln(x)$ is the logarithm with base $e$, so by the definition of logarithms, if $\ln(x) = y$, this means that $e$ raised to the power of $y$ equals $x$. In formula terms, if $\log_{b}(a)=c$, then $b^{c}=a$. For natural logarithm, $b = e$, so if $\ln(x)=y$ (which is $\log_{e}(x)=y$), then by the logarithmic - exponential conversion formula, we have $x = e^{y}$.

Step2: Match with the given options

Looking at the options, option A is $x = e^{y}$, which matches the result we got from converting the logarithmic equation $\ln(x)=y$ to its equivalent exponential form.

Answer:

A. $x = e^{y}$