The problem presented in the image is:

Solve the exponential equation $7^x = 143$ by writing it in logarithmic form, then using a calculator to solve to two decimal places.

Step-by-Step Solution:

1. Rewrite the Equation in Logarithmic Form: To solve $7^x = 143$ for $x$, take the logarithm of both sides. Using the property of logarithms, we get: $x = \log_7(143)$

2. Convert to a Common Logarithmic Base: Since most calculators do not have a base-7 logarithm, we use the change of base formula: $x = \frac{\log(143)}{\log(7)}$

3. Calculate Using a Calculator: Now, calculate the values:

   • $\log(143) \approx 2.1553$
   • $\log(7) \approx 0.8451$

   So, $x = \frac{2.1553}{0.8451} \approx 2.55$

Final Answer:

$x \approx 2.55$

Would you like further details on any part of the solution?

Here are some related questions for further understanding:

1. How do you solve exponential equations with different bases?
2. What is the change of base formula for logarithms and why is it useful?
3. How can logarithmic functions be applied in real-world problems?
4. What are the different properties of logarithms?
5. How do you verify solutions for exponential equations?

Tip: When converting logarithms to a common base, ensure you use precise values for better accuracy in the final result.