We need to solve the equation:

\[
6.6 \times 10^x = 4
\]

### Step 1: Isolate \(10^x\)
Divide both sides by 6.6:

\[
10^x = \frac{4}{6.6}
\]

Simplify:

\[
10^x = \frac{40}{66} = \frac{20}{33} \approx 0.6061
\]

### Step 2: Apply Logarithm
Take the logarithm (base 10) on both sides:

\[
\log(10^x) = \log(0.6061)
\]

Using the logarithm property \(\log(10^x) = x\):

\[
x = \log(0.6061)
\]

Using a calculator:

\[
x \approx -0.217
\]

### Final Answer:
\[
x \approx -0.217
\]

---

Would you like a more detailed explanation or alternative solving methods?  

Here are some related questions to explore:  

1. How do logarithmic properties help in solving exponential equations?  
2. What are different methods to approximate logarithmic values?  
3. Can this equation be solved using natural logarithms instead of base 10?  
4. How do you check your solution for an exponential equation?  
5. What are some real-world applications of logarithmic equations?  

**Tip:** Always check your solution by substituting it back into the original equation!

Learn how to solve the exponential equation 6.6(10^x) = 4 using logarithmic properties. This step-by-step solution covers key concepts such as isolating exponential terms, applying logarithms, and using log rules. Suitable for students in Grades 9-12.

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