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Given , $$3^{x}-3^{x-1}=486$$
$$3^{x}-\frac{3^{x}}{3}=486$$
Taking $$3^{x}$$ as common
$$3^{x}(1- \frac{1}{3})=486$$
$$3^{x}=729$$
$$3^{x}=3^{6}$$
Hence , x = 6
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