Bài 7:

1) \(2x - 135 = 3^7 \cdot 3^4\)

\(2x = 3^{11} + 135\)

\(x = \frac{3^{11} + 135}{2}\)

2) \(12x - 56 = 2^4 \cdot 2^2\)

\(12x = 2^6 + 56\)

\(x = \frac{2^6 + 56}{12}\)

3) \(6x - 31 = 5^6 \cdot 5^5\)

\(6x = 5^{11} + 31\)

\(x = \frac{5^{11} + 31}{6}\)

4) \(x - 115 = 4^6 \cdot 2^8\)

\(x = 4^6 \cdot 2^8 + 115\)

5) \(8x - 15 = 5^2 \cdot 3^0\)

\(8x = 5^2 + 15\)

\(x = \frac{5^2 + 15}{8}\)

6) \(3x - 25 = 6^3 \cdot 3^3\)

\(3x = 6^3 \cdot 3^3 + 25\)

\(x = \frac{6^3 \cdot 3^3 + 25}{3}\)

7) \(5x + 22 = 2^3 \cdot 3^2\)

\(5x = 2^3 \cdot 3^2 - 22\)

\(x = \frac{2^3 \cdot 3^2 - 22}{5}\)

8) \(3x + 22 = 7^9 \cdot 7^8\)

\(3x = 7^{17} - 22\)

\(x = \frac{7^{17} - 22}{3}\)

9) \(10x - 21 = 9^5 \cdot 3^8\)

\(10x = 9^5 \cdot 3^8 + 21\)

\(x = \frac{9^5 \cdot 3^8 + 21}{10}\)

10) \(4x + 12 = 4^2 \cdot 2^1\)

\(4x = 4^2 \cdot 2^1 - 12\)

\(x = \frac{4^2 \cdot 2^1 - 12}{4}\)

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Bài 8:

1) \( (x - 140) : 7 = 3^3 - 2^3 \cdot 3\)

\(x - 140 = 7(3^3 - 2^3 \cdot 3)\)

\(x = 140 + 7(3^3 - 2^3 \cdot 3)\)

2) \((15 + x) : 3 = 3^{15} : 3^{12}\)

\(15 + x = 3^{3}\)

\(x = 3^3 - 15\)

3) \(6(x + 2^3) + 40 = 100\)

\(6x + 48 + 40 = 100\)

\(6x = 100 - 88\)

\(x = 2\)

4) \(2^{x + 3^2} - 5 = 55\)

\(2^{x + 9} = 60\)

Solve for \(x\).

5) \(10 + 2(x - 3) = 4^5 : 4^3\)

\(2(x - 3) = 4^2 - 10\)

\(2x - 6 = 6\)

\(2x = 12\)

\(x = 6\)

6) \(4(x - 5) - 2^3 = 2^4 \cdot 3\)

\(4x - 20 - 8 = 48\)

\(4x = 76\)

\(x = \frac{76}{4}\)

7) \(7^2 - 7(13 - x) = 14\)

Solve for \(x\).

8) \(240 : (x - 5) = 2^5 \cdot 2 - 20\)

\(240 = (x - 5)(32 - 20)\)

Solve for \(x\).

9) \(12(x - 2) - 39 = 3^2\)

\(12x - 24 - 39 = 9\)

\(12x = 72\)

\(x = 6\)

10) \(20 : (1 + x) = 2^2 \cdot 5\)

\(20 = (1 + x) \cdot 20\)

\(x = \frac{20}{20} - 1 = 0\)