Solve the exponential equation $3 \times 2^{x+1} = 24$ without using logarithms.

1. Problem Description

Solve the exponential equation $3 \times 2^{x+1} = 24$ without using logarithms.

2. Solution Steps

We are given the equation $3 \times 2^{x+1} = 24$.

First, we divide both sides of the equation by 3:

$$2^{x+1} = \frac{24}{3}$$

$$2^{x+1} = 8$$

Now, we can write 8 as a power of 2:

$$8 = 2^3$$

So we have:

$$2^{x+1} = 2^3$$

Since the bases are equal, we can equate the exponents:

$$x+1 = 3$$

Subtract 1 from both sides:

$$x = 3 - 1$$

$$x = 2$$

3. Final Answer

The solution to the equation is $x = 2$.