To solve the equation $3^x = 8$, we need to find the value of $x$.

Since 8 is not a power of 3, we can solve this equation using logarithms. Here are the steps:

1. Take the natural logarithm (or logarithm to any base) of both sides: $\ln(3^x) = \ln(8)$

2. Use the power rule of logarithms, which states $\ln(a^b) = b \ln(a)$: $x \ln(3) = \ln(8)$

3. Solve for $x$: $x = \frac{\ln(8)}{\ln(3)}$

Using a calculator to find the natural logarithms:

• $\ln(8) \approx 2.0794$
• $\ln(3) \approx 1.0986$

Therefore, $x \approx \frac{2.0794}{1.0986} \approx 1.8928$

So, the value of $x$ that satisfies $3^x = 8$ is approximately $1.8928$.

Would you like more details or have any questions?

Here are some related questions to explore:

1. What is the general method for solving exponential equations?
2. How can we solve $2^x = 10$?
3. How do logarithms help in solving exponential equations?
4. What is the relationship between logarithms and exponents?
5. Can we use a different logarithm base to solve $3^x = 8$?
6. How would you solve $3^x = 8$ using common logarithms (base 10)?
7. What are some real-life applications of solving exponential equations?
8. What are the properties of logarithms that are useful in solving equations?

Tip: Remember that logarithms are powerful tools for solving equations involving exponential expressions, and understanding their properties can greatly simplify complex calculations.