a) `2^(3x + 2) = 4^(x+5)`
`⇒ (2^3)^x . 4 = 4^x . 4^5`
`⇒ 8^x . 4 = 4^x . 1024`
`⇒ 2^x . 4^x . 4 = 2^x . 2^x . 2^10`
`⇒ 2^x . 2^x . 2^x . 2^2 = 2^x . 2^x . 2^10`
`⇒ 2^x . 2^x . 2^(x+2) = 2^x . 2^x . 2^10`
`⇒ 2^(x+2) = 2^10`
`⇒ x + 2 = 10`
`⇒ x = 8`
b) `3^(2x - 1) = 243`
`⇒ 3^(2x - 1) = 3^5`
`⇒ 2x - 1 = 5`
`⇒ 2x = 6`
`⇒ x = 3`
c) `2^x + 2^(x+3) = 144`
`⇒ 2^x + 2^x . 2^3 = 144`
`⇒ 2^x . (1 + 8) = 144`
`⇒ 2^x . 9 = 144`
`⇒ 2^x = 144 : 9`
`⇒ 2^x = 16`
`⇒ x = 4`
