Let's break down the expression step by step:

The given expression is:

\[
4^4 \log{5} + 3^3 \log{4}
\]

### Step 1: Calculate the powers of 4 and 3
First, calculate the powers:

\[
4^4 = 4 \times 4 \times 4 \times 4 = 256
\]
\[
3^3 = 3 \times 3 \times 3 = 27
\]

### Step 2: Substitute these values into the expression:
\[
256 \log{5} + 27 \log{4}
\]

### Step 3: Use logarithmic values
Now, using approximate values for the logarithms:
\[
\log{5} \approx 0.69897
\]
\[
\log{4} \approx 0.60206
\]

### Step 4: Multiply
Now, multiply the values:

\[
256 \times 0.69897 \approx 178.53632
\]
\[
27 \times 0.60206 \approx 16.25562
\]

### Step 5: Add the results
Now, add the two results together:

\[
178.53632 + 16.25562 = 194.79194
\]

So, the value of the expression is approximately:

\[
\boxed{194.79}
\]

---

Would you like a deeper explanation or details on any step?

Here are some related questions for practice:
1. Evaluate \(5^3 \log 7 + 2^5 \log 2\).
2. Simplify \(2^6 \log 3 + 3^2 \log 2\).
3. Find the value of \(x\) if \(x^3 \log 5 = 100\).
4. What is the value of \(\log 10\)?
5. Use properties of logarithms to simplify \(\log(50) + \log(2)\).

**Tip:** Remember, logarithmic rules can simplify complex expressions when combined with exponentiation!

Explore a detailed solution to the mathematical expression 4⁴log5 + 3³log4. Learn about exponentiation and logarithms with step-by-step instructions, suitable for high school students (Grades 9-12).

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