Question

\(2^{x+2}\cdot3^{x+1}\cdot5^x=10800\)

Answer 1

\(2^{x+2}\cdot3^{x+1}\cdot5^x=10800\\\Rightarrow2^x\cdot2^2\cdot3^x\cdot3\cdot5^x=10800\\\Rightarrow(2^x\cdot3^x\cdot5^x)\cdot(2^2\cdot3)=10800\\\Rightarrow(2\cdot3\cdot5)^x\cdot(4\cdot3)=10800\\\Rightarrow30^x\cdot12=10800\\\Rightarrow30^x=10800:12\\\Rightarrow30^x=900\\\Rightarrow30^x=30^2\\\Rightarrow x=2\)

Answer 2

\(2^{x+2}.3^{x+1}.5^x=10800\\ \Leftrightarrow2^x.2^2.3^x.3.5^x=10800\\ \Leftrightarrow12.\left(2.3.5\right)^x=10800\\ \Leftrightarrow12.30^x=10800\\ \Leftrightarrow30^x=\dfrac{10800}{12}=900=30^2\\ Vậy:x=2\)