(5/2)^x-1=4/25

(5/2)^x - 1  =  4/25

Add 1 to both sides:

(5/2)^x  =  29/25

To solve an equation with the variable in the exponent, use logs:

log(5/2)^x  =  log(29/25)

An exponent in a log expression comes out as a multiplier:

x · log(5/2)  =  log(29/25)

Divide both sides by log(5/2):

x  =  log(29/25) / log(5/2)

x  =  0.162  (approximately)

5/2^x-1=4/25

5/2^x-1= 5/2 ^-2

x-1=-2

x=1