Question

Solve each of the following equations for x.
2^x − 1 = 0

Answer 1

The solution to the equation is x = 0

Explanation:

Hi there!

First, let´s write the equation:

2ˣ - 1 = 0

To solve it for x, let´s add 1 to both sides of the equation:

2ˣ = 1

Apply log to both sides of the equation

log(2ˣ) = log(1)

Apply logrithm property: log(2ˣ) = x log(2)

x log(2) = log(1)

x log(2) = 0

x = 0

The solution is x = 0

Let´s check the solution:

2ˣ - 1 = 0

x = 0

2⁰ - 1 = 0

1 - 1 = 0

0 = 0

The solution is correct!

Have a nice day!