We are solving the expression:

$\log(5x) + \log(4) + \log(x+4)$

Step 1: Apply the logarithmic property

Using the property of logarithms: $\log(a) + \log(b) = \log(a \cdot b)$ we can combine the terms:

$\log(5x) + \log(4) + \log(x+4) = \log(5x \cdot 4 \cdot (x+4))$

Step 2: Simplify the expression

Simplify the product inside the logarithm:

$\log(5x \cdot 4 \cdot (x+4)) = \log(20x(x+4))$

Final Answer:

$\log(20x(x+4))$

This is the simplified logarithmic expression. Let me know if you’d like to proceed further with any calculations or solve for $x$ under specific conditions.

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Follow-Up Questions:

1. Do you want to evaluate this expression for specific values of $x$?
2. Would you like to explore the domain of this logarithmic expression?
3. Should we expand $20x(x+4)$ or leave it in factored form?
4. Do you want to see how this applies in solving equations involving logs?
5. Should I demonstrate graphing $\log(20x(x+4))$?

Tip:

Always check the domain of logarithmic expressions: the arguments inside the logarithm must be positive.