Question

1)6.8^x-1+8^x+1=6.8¹⁹+8²¹                2)5.2^x+3.2^x+2=5.2⁵+3.2⁷

3)4.3^x-1+2.3^x+2=4.3⁶+2.3⁹                        4)11.6^x-1+2.6^x+1=11.6¹¹+2.6¹³

Answer 1

1) 6.8^(x - 1) + 8^(x + 1) = 6.8¹⁹ + 8²¹

8^(x - 1).(6 + 8²) = 8¹⁹.(6 + 8²)

8^(x - 1) = 8¹⁹

x - 1 = 19

x = 19 + 1

x = 20

2) 5.2^x + 3.2^(x + 2) = 5.2⁵ + 3.2⁷

2^x.(5 + 3.2²) = 2⁵.(5 + 3.2²)

2^x = 2⁵

x = 5

3) 4.3^(x - 1) + 2.3^(x + 2) = 4.3⁶ + 2.3⁹

3^(x - 1).(4 + 2.3³) = 3⁶.(4 + 2.3³)

3^(x - 1) = 3⁶

x - 1 = 6

x = 6 + 1

x = 7

4) 11.6^(x - 1) + 2.6^(x + 1) = 11.6¹¹ + 2.6¹³

6^(x - 1).(11 + 2.6²) = 6¹¹.(11 + 2.6²)

6^(x - 1) = 6¹¹

x - 1 = 11

x = 11 + 1

x = 12