SELESAIKAN SETIAP PERSAMAAN EKSPONENSIAL BERIKUT. bantu in kak, jgn sembarangan yaa

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SELESAIKAN SETIAP PERSAMAAN EKSPONENSIAL BERIKUT. bantu in kak, jgn sembarangan yaa

SELESAIKAN SETIAP PERSAMAAN EKSPONENSIAL BERIKUT. bantu in kak, jgn sembarangan yaa

Sifat Eksponensial yang digunakan:

▪︎a^{m+n} = a^{m} . a^{n}

▪︎a^{m-n} = frac{a^{m}}{a^{n}}

▪︎(a^{m})^{n} = a^{m times n}

Sifat Operasi yang digunakan:

Distributif: (a.b) + (a.c) = a . (b + c)

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a.)

2^{x} + 2^{x+3} = 72

2^{x} + 2^{x} . 2^{3} = 72

2^{x} + 2^{x} . 8 = 72

2^{x} . 1 + 2^{x} . 8 = 72

2^{x} (1 + 8) = 72

2^{x} (9) = 72

2^{x} = 8

2^{x} = 2^{3}

x = 3

b.)

3^{x} + 3^{x+2} = 90

3^{x} + 3^{x} . 3^{2} = 90

3^{x} + 3^{x} . 9 = 90

3^{x} . 1 + 3^{x} . 9 = 90

3^{x} (1 + 9) = 90

3^{x} (10) = 90

3^{x} = 9

3^{x} = 3^{2}

x = 2

c.)

4^{x+1} + 2^{2x} = 20

(2^{2})^{x+1} + 2^{2x} = 20

2^{2(x+1)} + 2^{2x} = 20

2^{2x+2} + 2^{2x} = 20

2^{2x} . 2^{2} + 2^{2x} = 20

2^{2x} . 4 + 2^{2x} = 20

2^{2x} . 4 + 2^{2x} . 1 = 20

2^{2x} (4 + 1) = 20

2^{2x} (5) = 20

2^{2x} = 4

2^{2x} = 2^{2}

2x = 2

x = 1

d.)

2^{x} - 2^{x-2} = -12

2^{x} - frac{2^{x}}{2^{2}} = -12

2^{x} - frac{2^{x}}{4} = -12

Kedua ruas dikalikan 4

2^{x}(4) - 2^{x} = -12(4)

2^{x} . 4 - 2^{x} . 1 = -48

2^{x} (4 - 1) = -48

2^{x} (3) = -48

2^{x} = -16

2^{x} = -2^{4}

Tidak bisa ditentukan hasilnya.

Jika soalnya 2^{x} - 2^{x-2} = 12 ada hasilnya

2^{x} - 2^{x-2} = 12

2^{x} - frac{2^{x}}{2^{2}} = 12

2^{x} - frac{2^{x}}{4} = 12

Kedua ruas dikalikan 4

2^{x}(4) - 2^{x} = 12(4)

2^{x} . 4 - 2^{x} . 1 = 48

2^{x} (4 - 1) = 48

2^{x} (3) = 48

2^{x} = 16

2^{x} = 2^{4}

x = 4

e.)

3^{x^{2}-5} - 9^{x-1} = 0

3^{x^{2}-5} = 9^{x-1}

3^{x^{2}-5} = (3^{2})^{x-1}

3^{x^{2}-5} = 3^{2(x-1)}

3^{x^{2}-5} = 3^{2x-2}

x^{2}-5 = 2x-2

x^{2}-5-2x+2 = 0

x^{2}-2x-3 = 0

(x-3)(x+1) = 0

x-3 = 0

x = 3

atau

x+1 = 0

x = -1

f.)

5^{x^{2}+3} - 25^{2x} = 0

5^{x^{2}+3} = 25^{2x}

5^{x^{2}+3} = (5^{2})^{2x}

5^{x^{2}+3} = 5^{2(2x)}

5^{x^{2}+3} = 5^{4x}

x^{2}+3 = 4x

x^{2}+3-4x = 0

x^{2}-4x+3 = 0

(x-3)(x-1) = 0

x-3 = 0

x = 3

atau

x-1 = 0

x = 1

Semoga Membantu.