Question

solve 2^x+3 = 4^x-1 find value of x​

Answer 1

Answer:

5.

Step-by-step explanation:

⇒ 2^( x + 3 ) = 4^( x - 1 )

⇒ 2^( x + 3 ) = ( 2^2 )^( x - 1 )

⇒ 2^( x + 3 ) = 2^{ 2( x - 1 ) }

⇒ 2^( x + 3 ) = 2^( 2x - 2 )

        Powers of two, both sides, must be equal.

⇒ x + 3 = 2x - 2

⇒ 3 + 2 = 2x - x

⇒ 5 = x

      Hence the required value of x is 5.

 Few terms used here :

          4 = 2^2  { in 2nd step, RHS }

          ( a^n )^m = a^( nm )     { in 3nd step, RHS }