a town predicts that its population will double in $\frac{e^{ln10}}{2ln e}$ years. simplify the expression…
a town predicts that its population will double in $\frac{e^{ln10}}{2ln e}$ years. simplify the expression. in how many years will the population of the town double?
Answer
Explanation:
Step1: Recall logarithmic and exponential properties
Recall that $e^{\ln x}=x$ and $\ln e = 1$.
Step2: Simplify the numerator
Since $e^{\ln 10}=10$ (by the property $e^{\ln x}=x$), the expression becomes $\frac{10}{2\ln e}$.
Step3: Simplify the denominator
Since $\ln e = 1$, then $2\ln e=2\times1 = 2$.
Step4: Calculate the final value
$\frac{10}{2}=5$.
Answer:
5