tolong dijawab ya 2 soal matematika ini (nomor 9 dan 10). materinya ttg sistem persamaan eksponen kelas 12 SMA. trims banyak!

Cara ada di foto / lampiran

Jawaban:

9.d. 3

10. b. -1 – ⁵log2

Penjelasan dengan langkah-langkah:

no.9

64(4ʸ) = 16ˣ

4³.4ʸ = (4²)ˣ

4ʸ ⁺ ³ = 4²ˣ

2x = y + 3

y = 2x – 3 ……………(1)

3ʸ = 4(3ˣ ⁻ ²) – 1

3²ˣ ⁻ ³ = 4(3ˣ ⁻ ²) – 1

3⁻³ . 3²ˣ = 4(3⁻² . 3ˣ) – 1

3²ˣ/27 = 4/9(3ˣ) – 9/9

3²ˣ/3 = 4. 3ˣ – 9

3²ˣ = 12. 3ˣ – 27

(3ˣ)² – 12.3ˣ + 27 = 0

misal a = 3ˣ

a² – 12a + 27 = 0

(a – 9)(a – 3) = 0

a = 3

3ˣ = 3

3ˣ = 3¹

x = 1

y = 2x – 3

y = 2(1) – 3

y = – 1

(x + y) = 1 + (-1) = 0 (tidak ada dipilihan)

a = 9

3ˣ = 9

3ˣ = 3²

x = 2

y = 2x – 3

y = 2(2) – 3

y = 1

(x + y) = 2 + 1 = 3……..jawaban (d)

.

no.10

2(25)ˣ ⁺ ¹ + 5ˣ ⁺ ² – 3 = 0

2(25)ˣ ⁺ ¹ + 5ˣ ⁺ ² = 3

2(25)ˣ ⁺ ¹ + 5.5ˣ ⁺ ¹ = 3

2(5ˣ ⁺ ¹)² + 5.5ˣ ⁺ ¹ = 3

misal 5ˣ ⁺ ¹ = a

2a² + 5a = 3

2a² + 5a – 3 = 0

(2a – 1)(a + 3) = 0

a = -3

(5ˣ ⁺ ¹) = -3 tidak memenuhi syarat seharusnya (5ˣ ⁺ ¹) > 0

2a = 1

a = 1/2

(5ˣ ⁺ ¹) = 1/2

⁵log 5ˣ ⁺ ¹ = ⁵log2⁻¹

(x + 1)⁵log5 = -⁵log2

(x + 1) = -⁵log2

x = – 1 – ⁵log2 ………jawaban (b)