Question

Tìm x:

3^x+2 - 3^x - 9⁵ = 27³ . 5

Answer 1

\(3^{x+2}-3^x-9^5=27^3\cdot5\)

\(\Rightarrow3^{x+2}-3^x-\left(3^2\right)^5=\left(3^3\right)^3\cdot5\)

\(\Rightarrow3^{x+2}-3^x-3^{10}=3^9\cdot5\)

\(\Rightarrow3^{x+2}-3^x=3^9\cdot5+3^{10}\)

\(\Rightarrow3^x\cdot3^2-3^x\cdot1=3^9\cdot\left(5+3\right)\)

\(\Rightarrow3^x\left(9-1\right)=3^9\cdot8\)

\(\Rightarrow3^x\cdot8=3^9\cdot8\)

\(\Rightarrow3^x=3^9\)

\(\Rightarrow x=9\)

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