Jawaban:

Tentukan himpunan penyelesaian dari setiap persamaan eksponen berikut!

a) \: {7}^{2x - 6} = 1a)72x−6=1

→ x = 3

b) \: 13 ^{ {x}^{2} - 5x - 14} = 1b)13x2−5x−14=1

→ x = -2 atau x = 7

c) \: {2}^{3x - 8} = 16c)23x−8=16

→ x = 4

d) \: {7}^{ {x}^{2} - 2x - 6} = 49d)7x2−2x−6=49

→ x = -2 atau x = 4

e) \: {36}^{x + 5} = ( \frac{1}{216} ) {}^{x - 1}e)36x+5=(2161)x−1

→ x = -7/5

f) \: {3}^{3x - 4} = ( \frac{1}{27} ) {}^{x - 3}f)33x−4=(271)x−3

→ x = 2 1/6

g) \: {3}^{3x - 4} = {81}^{x - 2}g)33x−4=81x−2

→ x = 4

h) \: {49}^{x + 3} = 7 {}^{ {x}^{2} - 3x - 8 }h)49x+3=7x2−3x−8

→ x = -2 atau x = 7

Penjelasan dengan langkah-langkah:

.

a) \: {7}^{2x - 6} = 1a)72x−6=1

{7}^{2x - 6} = {7}^{0}72x−6=70

2x - 6 = 02x−6=0

2x = 62x=6

x = \frac{6}{2}x=26

x = 3x=3

.

b) \: {13}^{ {x}^{2} - 5x - 14 } = 1b)13x2−5x−14=1

{13}^{ {x}^{2} - 5x - 14} = {13}^{0}13x2−5x−14=130

{x}^{2} - 5x - 14 = 0x2−5x−14=0

(x + 2)(x - 7) = 0(x+2)(x−7)=0

x + 2 = 0x+2=0

x = - 2x=−2

atau

x - 7 = 0x−7=0

x = 7x=7

.

c) \: {2}^{3x - 8} = 16c)23x−8=16

{2}^{3x - 8} = {2}^{4}23x−8=24

3x - 8 = 43x−8=4

3x = 4 + 83x=4+8

3x = 123x=12

x = 4x=4

.

d) \: {7}^{ {x}^{2} - 2x - 6} = 49d)7x2−2x−6=49

{7}^{ {x}^{2} - 2x - 6} = {7}^{2}7x2−2x−6=72

{x}^{2} - 2x - 6 = 2x2−2x−6=2

{x}^{2} - 2x - 6 - 2 = 0x2−2x−6−2=0

{x}^{2} - 2x - 8 = 0x2−2x−8=0

(x + 2)(x - 4) = 0(x+2)(x−4)=0

x + 2 = 0x+2=0

x = - 2x=−2

atau

x - 4 = 0