\(3^x+5.3^{x-1}=72\)
=> \(3^{x-1}.3+5.3^{x-1}=72\)
=> \(3^{x-1}.\left(3+5\right)=72\)
=> \(3^{x-1}.8=72\)
=> \(3^{x-1}=72:8\)
=> \(3^{x-1}=9\)
=> \(3^{x-1}=3^2\)
=> \(x-1=2\)
=> \(x=2+1\)
=> \(x=3\)
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