The expression $4 \log_4(2x+3)$ can be simplified using logarithmic properties. Here’s how it works:

1. Start with the expression: $4 \log_4(2x+3)$

2. Use the Power Rule of Logarithms, which states that $a \cdot \log_b(M) = \log_b(M^a)$. Apply it here to bring the 4 inside the logarithm: $\log_4((2x+3)^4)$

Therefore, the expression $4 \log_4(2x+3)$ simplifies to: $\log_4((2x+3)^4)$

Would you like further details on logarithmic properties or any additional explanation on simplifying expressions?

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Related Questions

1. How would you solve for $x$ if $4 \log_4(2x+3) = 8$?
2. What is the value of $4 \log_4(2x+3)$ when $x = 1$?
3. Can you convert $\log_4((2x+3)^4)$ into a different logarithmic base, such as base 10?
4. How do logarithmic rules apply when the base of the log changes, such as from 4 to 2?
5. What are some practical applications of logarithmic functions in real-world scenarios?

Tip: Remember, logarithmic identities can simplify complex expressions, especially when powers or products are involved.