`5^{3}.5^{x-2}=125^{2}`
`=>5^{3+x-2}=(5^{3})^{2}`
`=>5^{x+1}=5^{3.2}=5^{6}`
`=>x+1=6`
`=>x=5`
\(5^3.5^{x-2}=125^2\)
\(\Leftrightarrow125.5^{x-2}=125^2\)
\(\Leftrightarrow5^{x-2}=125\)
\(\Leftrightarrow x-2=3\Leftrightarrow x=5\)
53 . 5x-2 = 1252
=>53+x-2 = (53)2
=>53+x-2 = 56
=>5x+1 = 53.2 = 56
=> x+1 = 6
x = 5
=> x=5