Solve 25x 62516SolutionGiven that 2 5 x 625 16 2 5

Solution

Given that

( 2 / 5 ) ^x = 625 / 16

   ( 2 / 5 ) ^x = 5⁴ / 2⁴

  ( 2 / 5 ) ^x = ( 5 / 2 ) ⁴

   ( 2 / 5 ) ^x = ( 2 / 5 ) ^-4

If bases are equal then powers to be equal.

Hence,

x = -4