Question

question 7 of 10
which expressions are equivalent to the one below? check all that apply.
$ln(e^5)$

a. $5e$

b. $1$

c. $5$

d. $5 cdot ln e$

Explanation:

Step1: Recall logarithm power rule

The power rule of logarithms states that $\ln(a^b) = b \cdot \ln(a)$. Applying this to $\ln(e^5)$, we get $\ln(e^5)=5\cdot\ln(e)$.

Step2: Recall natural log of e

We know that $\ln(e) = 1$ because the natural logarithm function $\ln(x)$ is the inverse of the exponential function $e^x$, so $\ln(e)=1$.

Step3: Substitute $\ln(e)$ value

Substituting $\ln(e) = 1$ into $5\cdot\ln(e)$, we have $5\cdot1 = 5$. Also, from Step1, we have the expression $5\cdot\ln(e)$ which is equivalent to $\ln(e^5)$.

Answer:

C. 5, D. $5 \cdot \ln e$