Question

a town predicts that its population will double in \\(\frac{e^{\ln 10}}{2\ln e}\\) years. simplify the expression. in how many years will the population of the town double? done

Explanation:

Step1: Simplify \( e^{\ln 10} \)

Recall the property of logarithms and exponentials: \( e^{\ln x}=x \). So, \( e^{\ln 10} = 10 \).

Step2: Simplify \( \ln e \)

Recall that \( \ln e = 1 \) (since the natural logarithm of the base \( e \) is 1).

Step3: Substitute and simplify the fraction

Substitute the simplified values into the expression \( \frac{e^{\ln 10}}{2\ln e} \). We get \( \frac{10}{2\times1} \).
Simplify \( \frac{10}{2} = 5 \).

Answer:

5