If $1$ , $\log_{9}(3^{x+1} + 2)$, $\log_{3}(4⋅3^{x}-1)$ are in A.P. , then $x$ equals ?
2026-03-27 15:17:53.1774624673
Finding value of $x$ in an A.P.
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$$2\log_{9}(3^{x+1} + 2)=1+\log_{3}(4⋅3^{x}-1)$$ We have $$\log_{3}(3^{x+1} + 2)=\log_{3}(4⋅3^{x+1}-3)$$ therefore $$3^{x+1} + 2=4⋅3^{x+1}-3\implies 3^{x+2}=5$$ $$x=-2+\log_{3}(5)$$