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:

⚡ Using what you learned: Evaluating Logarithmic Expressions

Step 1: Simplify the numerator

Evaluate the exponential expression with a natural logarithm in the exponent:

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

Step 2: Simplify the denominator

Evaluate the natural logarithm of \( e \):

$$ \ln(e) = 1 $$

Multiply by the coefficient:

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

Step 3: Divide the simplified terms

Substitute the simplified numerator and denominator back into the fraction:

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

Answer:

5