\(2^{x+2}\cdot3^{x+1}\cdot5^x=10800\)
\(2^x\cdot2^2\cdot3^x\cdot3\cdot5^x=10800\)
\(4\cdot3\cdot2^x\cdot3^x\cdot5^x=10800\)
\(12\cdot\left(2\cdot3\cdot5\right)^x=10800\)
\(12\cdot30^x=10800\)
\(30^x=10800:12\)
\(30^x=900\)
\(30^x=30^2\)
=> x = 2