To solve the equation \( 11 \log(x + 7) = 7 \), follow these steps:

1. **Isolate the logarithmic term:**
   \[
   \log(x + 7) = \frac{7}{11}
   \]

2. **Rewrite the equation in exponential form:**
   Since \( \log(x + 7) \) refers to the logarithm with base 10 (common logarithm), the equation can be rewritten as:
   \[
   x + 7 = 10^{\frac{7}{11}}
   \]

3. **Subtract 7 from both sides:**
   \[
   x = 10^{\frac{7}{11}} - 7
   \]

4. **Calculate \( 10^{\frac{7}{11}} \):**
   \[
   10^{\frac{7}{11}} \approx 2.051
   \]
   So:
   \[
   x \approx 2.051 - 7 = -4.949
   \]

Thus, the solution is approximately \( x \approx -4.949 \).

Would you like further details or have any questions?

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Here are five related questions to deepen your understanding:

1. How do you solve logarithmic equations with different bases?
2. What is the general method to convert a logarithmic equation to an exponential form?
3. How do you handle logarithmic equations with multiple logarithms?
4. What is the importance of the domain in logarithmic functions?
5. How do you solve exponential equations that involve logarithms?

**Tip:** Always check if the argument inside the logarithm is positive, as the logarithm of a non-positive number is undefined.

Discover how to solve the logarithmic equation 11 log(x + 7) = 7 with a step-by-step guide. This problem explores algebraic concepts like logarithms and exponential functions, using the formula log_b(x) = y -> x = b^y. Suitable for students in Grades 9-11.

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