https://file.aiquickdraw.com/mathbot/file/1727624006298bd5dovfb.jpg

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.

Learn how to solve the logarithmic equation log2(3x + 2) = 4 by converting it into exponential form and solving for x. This problem covers key concepts of logarithms and algebra, suitable for students in Grades 9-11.

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