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Let's solve the given equation step by step.

The equation is:

\[
3 \cdot 2^{\frac{x}{5}} = 150
\]

### Step 1: Isolate the exponential term

Divide both sides of the equation by 3:

\[
2^{\frac{x}{5}} = \frac{150}{3} = 50
\]

### Step 2: Take the logarithm of both sides

To solve for \(x\), we take the logarithm base 2 on both sides of the equation:

\[
\frac{x}{5} = \log_2(50)
\]

### Step 3: Solve for \(x\)

Now multiply both sides by 5 to solve for \(x\):

\[
x = 5 \log_2(50)
\]

### Conclusion

The correct answer is **Option D**: \(x = 5 \log_2(50)\).

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Would you like further details or have any other questions?

Here are 5 related questions:
1. How do you calculate logarithms of non-standard bases?
2. What properties of logarithms can simplify solving exponential equations?
3. How does logarithmic scaling differ between base 2 and base 10?
4. Can you convert logarithms from one base to another?
5. What are the applications of solving exponential equations in real-world problems?

**Tip:** When solving exponential equations, using logarithms can be extremely useful to simplify powers of numbers into more manageable expressions.

3 * 2^(x/5) = 150. Which of the following is the solution of the equation?

Learn how to solve the exponential equation 3 * 2^(x/5) = 150 using logarithms. Follow the step-by-step process, involving logarithmic properties and the change of base theorem, suitable for students in Grades 9-11.

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