\(3^{x-1}+3^{x+1}-1=89\)
\(3^{x-1}.\left(1+3^2\right)=89+1\)
\(3^{x-1}.10=90\)
\(3^{x-1}=90:10\)
\(3^{x-1}=9\)
\(3^{x-1}=3^2\)
\(x-1=2\)
\(x=2+1\)
\(x=3\)
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\(3^{x-1}+3^{x+1}-1=89\)
\(\Rightarrow3^x\cdot\left(3^{-1}+3^1\right)=89+1\)
\(\Rightarrow3^x\cdot\left(\dfrac{1}{3}+3\right)=90\)
\(\Rightarrow3^x\cdot\dfrac{10}{3}=90\)
\(\Rightarrow3^x=90:\dfrac{10}{3}\)
\(\Rightarrow3^x=27\)
\(\Rightarrow3^x=3^3\)
\(\Rightarrow x=3\)
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