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I will solve the exercises from the image you uploaded. Let's go through them one by one.

### a) \(\sqrt{16} - 4 \times 5 + 12 \div 3 =\)

First, solve the square root:
\[
\sqrt{16} = 4
\]

Now, perform the multiplication and division from left to right:
\[
4 - (4 \times 5) + \left(\frac{12}{3}\right)
\]
\[
4 - 20 + 4
\]

Finally, perform the addition and subtraction:
\[
(4 - 20) + 4 = -16 + 4 = -12
\]
So, the result is **\(-12\)**.

### b) \(20 \div 4 + 15 - 24 \div 8 \times 10 - 2 =\)

First, perform the division and multiplication from left to right:
\[
(20 \div 4) + 15 - \left(24 \div 8 \times 10\right) - 2
\]
\[
5 + 15 - (3 \times 10) - 2
\]
\[
5 + 15 - 30 - 2
\]

Finally, perform the addition and subtraction:
\[
(5 + 15) - 30 - 2 = 20 - 30 - 2 = -10 - 2 = -12
\]
So, the result is **\(-12\)**.

### c) \(-9 + 3 + \sqrt{11^2 - 7 + 17} - 12 \times 4 =\)

First, calculate inside the square root:
\[
\sqrt{11^2 - 7 + 17} = \sqrt{121 - 7 + 17} = \sqrt{131}
\]

Now, perform the multiplication and the addition/subtraction:
\[
-9 + 3 + \sqrt{131} - (12 \times 4)
\]
\[
-9 + 3 + \sqrt{131} - 48
\]
\[
-6 - 48 + \sqrt{131} = -54 + \sqrt{131}
\]

Since \(\sqrt{131}\) is an irrational number, the final result is **\(-54 + \sqrt{131}\)**.

### d) \(345 \div 15 = 3^x\)

We first simplify the division:
\[
345 \div 15 = 23
\]

Now, solve the equation \(23 = 3^x\). Taking the logarithm on both sides:
\[
\log(23) = x \log(3)
\]
\[
x = \frac{\log(23)}{\log(3)} \approx \frac{1.3617}{0.4771} \approx 2.855
\]
So, \(x \approx 2.86\).

### e) \(28 \div 2 - 20 + 2^2 \times 3 \sqrt{4 + 7} =\)

First, solve inside the square root and exponent:
\[
\sqrt{4 + 7} = \sqrt{11}, \quad 2^2 = 4
\]

Now, substitute and solve step by step:
\[
28 \div 2 - 20 + 4 \times 3 \times \sqrt{11}
\]
\[
14 - 20 + 12\sqrt{11}
\]
So, the final result is **\( -6 + 12\sqrt{11}\)**.

---

If you need a detailed explanation or have further questions, feel free to ask! 

Here are 5 related questions to practice:

1. What is the value of \(x\) if \(3^x = 81\)?
2. Simplify the expression \(\sqrt{50} - \sqrt{18}\).
3. Solve for \(x\): \(2^x = 32\).
4. Evaluate \(15 \div 3 \times 2^2\).
5. Find the value of \(x\) in the equation \(log(x) = 2\).

**Tip:** Always remember the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Explore how to solve arithmetic and algebraic equations step-by-step with detailed explanations. This problem set covers key concepts such as arithmetic operations, algebraic expressions, exponents, and square roots. Suitable for students in Grades 7-9.

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