f) 3ˣ⁺² + 3ˣ = 270 = 3³ x 10
3ˣ ( 3² + 1 ) = 3³ x 10
3ˣ x 10 = 3³ x 10 l : 10
3ˣ = 3³ = > x = 3
g)
3 x 2ˣ⁺² - 5 x 2 ˣ⁺¹ - 2ˣ = 2
2ˣ ( 3 x 2² - 5 x 2¹ - 1) = 2 ¹
2ˣ ( 12 - 10 - 1) = 2¹
2ˣ = 2¹ = > x = 1
h)
5ˣ⁺² - 2 x 5ˣ⁺¹ - 12 x 5ˣ = 375
5ˣ ( 5² - 2 x 5 - 12 x 1) = 375
5ˣ ( 25 - 10 - 12 ) = 375
5ˣ x 3 = 375
5ˣ = 375 : 3 = 125 = 5³ = > x = 3
i)
2ˣ x 3ˣ⁺¹ = ( 2 x 3 )ˣ x 3¹ = 108
= 6ˣ = 108 : 3 = 36 = 6² = > x = 2
j)
3ˣ⁺¹ x 5ˣ = 675
( 3 x 5 )ˣ x 3 = 675
15ˣ = 675 : 3 = 225 = 15² = > x = 2
