To solve the equation $\log_5 125 = x + 4$, we'll break it down step by step:

Step 1: Understand the logarithmic expression

The equation $\log_5 125$ represents the logarithm of 125 with base 5. This asks, "To what power must 5 be raised to get 125?"

Step 2: Solve the logarithm

We know that $5^3 = 125$. Therefore: $\log_5 125 = 3$ So, the equation becomes: $3 = x + 4$

Step 3: Solve for $x$

To isolate $x$, subtract 4 from both sides: $x = 3 - 4$ $x = -1$

Final Answer

The solution is: $x = -1$

Would you like any more details or have any questions?

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Related Questions:

1. How do you evaluate logarithms without a calculator?
2. What is the relationship between exponents and logarithms?
3. How do you solve logarithmic equations that involve multiple logs?
4. Can logarithms have negative bases?
5. What are the steps to graph a logarithmic function?

Tip: When dealing with logarithms, always remember that you can convert them to exponential form to make solving easier.