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?

Explanation:

Simplify the numerator

Using the Inverse Properties of Logarithms knowledge point

$$ e^{\ln(10)} = 10 $$

Simplify the denominator

Using the Inverse Properties of Logarithms knowledge point

$$ \ln(e) = 1 \implies 2\ln(e) = 2(1) = 2 $$

Evaluate the fraction

Using the Inverse Properties of Logarithms knowledge point

$$ \frac{e^{\ln(10)}}{2\ln(e)} = \frac{10}{2} = 5 $$

Answer:

A town predicts that its population will double in \(\frac{e^{\ln10}}{2\ln e}\) years.

Simplify the expression. In how many years will the population of the town double? <blank>5</blank>