Find nnn so that 811÷85=8−3×82n−18^{11} ÷ 8^5 = 8^{-3} \times 8^{2n-1}811÷85=8−3×82n−1.
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811÷85=8−3×82n−1⇒811−5=8−3+(2n−1)⇒86=8−3+2n−1⇒86=8−4+2n⇒6=−4+2n⇒6+4=2n⇒10=2n⇒n=102⇒n=58^{11} ÷ 8^5 = 8^{-3} \times 8^{2n-1}\\[1em] \Rightarrow 8^{11 - 5} = 8^{-3 + (2n-1)}\\[1em] \Rightarrow 8^{6} = 8^{-3 + 2n - 1}\\[1em] \Rightarrow 8^{6} = 8^{-4 + 2n}\\[1em] \Rightarrow 6 = -4 + 2n\\[1em] \Rightarrow 6 + 4 = 2n\\[1em] \Rightarrow 10 = 2n\\[1em] \Rightarrow n = \dfrac{10}{2} \\[1em] \Rightarrow n = 5811÷85=8−3×82n−1⇒811−5=8−3+(2n−1)⇒86=8−3+2n−1⇒86=8−4+2n⇒6=−4+2n⇒6+4=2n⇒10=2n⇒n=210⇒n=5
If 811÷85=8−3×82n−18^{11} ÷ 8^5 = 8^{-3} \times 8^{2n-1}811÷85=8−3×82n−1, then n=5n = 5n=5.
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