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			© h.hofstede (h.hofstede@hogeland.nl)

1.	a.	4 • 3^2x = 4 • (3²)^x = 4 • 9^x

	b.	0,5 • 4^x^{+ 2}= 0,5 • 4^x • 4² = 0,5 • 4^x • 16 = 8 • 4^x

	c.	3 • 2^2x • 2 = 3 • (2²)^x • 2 = 3 • 4^x • 2 = 6 • 4^x

	d.	5 • 4^x• 4^{x + 1} = 5 • 4^x • 4^x • 4¹ = 5 • 4^x+x • 4 = 20 • 4^2x= 20 • (4²)^x = 20 • 16^x

	e.	3 • 1,8²^x • 6 • 1,8^{x + 1} = 3 • 1,8^2x• 6 • 1,8^x • 1,8¹ = 18 • 1,8¹ • 1,8^2x • 1,8^x = 32,4 • 1,8^{2x + x}= 32,4 • 1,8^3x = 32,4 • (1,8³)^x = 32,4 • 5,832^x

	f.	0,2^{2x + 3} = 0,2^{2x •}0,2³ = (0,2²)^x• 0,008 = 0,008 • 0,04^x

	g.	20 • 3^{4x + 5} = 20 • 3^4x • 3⁵ = 20 • (3⁴)^x • 243 = 4860 • 81^x

	h.	2^x • 2²^x• 4 = 2^{x + 2x} • 4 = 2^3x • 4 = (2³)^x • 4 = 4 • 8^x

	i.	6^x • 3 • 6^x+1= 6^x • 3 • 6^x• 6¹ = 3 • 6 • 6^x • 6^x = 18 • 6^{x + x}= 18 • 6^2x = 18 • (6²)^x = 18 • 36^x

	j.	4 • 3^x + 3^{x + 2} = 4 • 3^x + 3^x • 3² = 4 • 3^x + 9 • 3^x= 13 • 3^x

2.	2^{4x + 1} = 4 • 4^x 2^{4x + 1} = 2² • (2²)^x 2^{4x + 1} = 2² • 2^2x2^{4x + 1}= 2^{2 + 2}^x 4x + 1 = 2 + 2x 2x = 1 x = ¹/₂ Dan is y = 2^{4 • -0,5 + 1} = 2^-1 = ¹/₂

3.

4.	3^{x + 7} • 9^{x + 4} = 27^{x + 5} 3^{x + 7} • (3²)^{(x + 4)} = (3³)^{(x + 5)}3^{x + 7} • 3^{2x + 8} = 3^{3x + 15} 3^{3x + 15} = 3^{3x + 15}3x + 15 = 3x + 15 dat geldt voor elke x, dus er zijn oneindig veel oplossingen.

5.	9^x- 2 · 3^x = 25 · 3^x 9^x = 27 · 3^x 3^2x = 3^{3 + x} 2x = 3 + x x = 3 dan is y = 675

6.	8⁸ = (2³)⁸ = 2²⁴ = 2^2•12 = (2²)¹² = 4¹² = 4^{4 • 3} = (4⁴)³ dus antwoord b)

7.	(2⁴)⁸ = 2³² (4²)⁸ = 4¹⁶ = (2²)¹⁶ = 2³²2^{16 •} 16²= 2¹⁶ • (2⁴)² = 2¹⁶ • 2⁸ = 2²⁴2¹⁶ • 2¹⁶ = 2³² 4⁸ • 4⁸ = (2²)⁸ • (2²)⁸ = 2¹⁶ • 2¹⁶ = 2³² de derde is anders dan de andere vier.

8.	5x^5x = 5(x^x)⁵ = 5 • 5⁵ = 5⁶