222k views
5 votes
E^(2x)-e^(x)-2=0 Round to the nearest hundredth if necessary.

User Funkifunki
by
8.3k points

1 Answer

4 votes

Answer:

Let's denote e^x as u.

The equation can be written as u^2 - u - 2 = 0.

Factoring the quadratic equation, we have (u - 2)(u + 1) = 0.

Setting each factor equal to zero, we obtain u - 2 = 0 and u + 1 = 0.

Solving the equations, we find u = 2 and u = -1.

Since e^x cannot be negative, we discard u = -1.

Hence, e^x = 2.

Taking the natural logarithm of both sides, we have x = ln(2).

Round to the nearest hundredth, x = 0.69. Answer: \boxed{0.69}.

Explanation:

User Lesyk
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories