Question

tim so nguyen x biet

5^x+1 - 5^x-1 = 600

3^x+1 - 3^x-2 = 702

Answer 1

\(5^{x+1}-5^{x-1}=600\)

\(\Leftrightarrow5^{x-1}\left(5^2-1\right)=600\)

\(\Leftrightarrow5^{x-1}=\frac{600}{24}=25\)

\(\Leftrightarrow5^{x-1}=5^2\Leftrightarrow x-1=2\)

\(\Leftrightarrow x=1\)

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\(3^{x+1}-3^{x-2}=702\)

\(\Leftrightarrow3^{x-2}\left(3^3-1\right)=702\)

\(\Leftrightarrow3^{x-2}=\frac{702}{26}=27\)

\(\Leftrightarrow3^{x-2}=3^3\Leftrightarrow x-2=3\)

\(\Leftrightarrow x=5\)

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