The equation in the image is:

$\log_2(3x + 2) = 4$

To solve for $x$:

Step 1: Rewrite the logarithmic equation in exponential form.

Since the base is 2, you can rewrite the equation as:

$3x + 2 = 2^4$

Step 2: Simplify the right-hand side.

$2^4 = 16$ So the equation becomes: $3x + 2 = 16$

Step 3: Solve for $x$.

First, subtract 2 from both sides: $3x = 14$

Then, divide both sides by 3: $x = \frac{14}{3} = 4.\overline{6}$

Step 4: Round to 4 decimal places (if necessary).

The value of $x$ is approximately: $x = 4.6667$

So, $x = \frac{14}{3}$ or approximately $4.6667$.

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. Solve $\log_3(2x + 1) = 5$.
2. What is the value of $x$ in $\log_5(4x - 7) = 3$?
3. Solve $\log_2(x^2 + 5x) = 6$.
4. Convert $\log_b(x + 3) = 7$ to exponential form.
5. What is $x$ in $\log_4(x + 2) = 3.5$?

Tip: When solving logarithmic equations, always rewrite the equation in exponential form to simplify the solution process.