b, ( 2x - 1 )²⁰²⁰ = ( 2x - 1 )²⁰¹⁹ c, 5ˣ + ¹ + 5ˣ+² = 750 d, 4ˣ - ¹ + 1²⁰¹⁹ = 257

`b) ( 2x - 1 )^2020 = ( 2x - 1 )^2019`

`( 2x - 1 )^2020 - ( 2x - 1 )^2019 = 0`

`( 2x - 1 )^2019 . ( 2x - 1 - 1 ) = 0`

`( 2x - 1 )^2019 . ( 2x - 2 ) = 0`

$\left[\begin{matrix} ( 2x - 1 )^{2019}=0\\ 2x - 2=0\end{matrix}\right.$

$\left[\begin{matrix} 2x - 1=0\\ 2x =2\end{matrix}\right.$

$\left[\begin{matrix} 2x=1\\ x=1\end{matrix}\right.$

$\left[\begin{matrix} x=\dfrac{1}{2}\\ x=1\end{matrix}\right.$

`c) 5^( x + 1 ) + 5^( x + 2 ) = 750`

`5^x . 5 + 5^x . 5^2 = 750`

`5^x . ( 5 + 5^2 ) = 750`

`5^x . 30 = 750`

`5^x = 25`

`5^x = 5^2`

`=> x = 2`

`d) 4^( x - 1 ) + 1^2019 = 257`

`4^x . 4 + 1 = 257`

`4^x . 4 = 257 - 1`

`4^x . 4 = 256`

`4^x = 64`

`4^x = 4^3`

`=> x = 3`