Question

5^(x)-5^(x-1)-5^(x-2)=2375

Answer 1

\(5^x-5^{x-1}-5^{x-2}=2375\\ \Leftrightarrow5^x-\dfrac{5^x}{5}-\dfrac{5^x}{25}=2375\\ \Leftrightarrow5^x\left(1-\dfrac{1}{5}-\dfrac{1}{25}\right)=2375\\ \Leftrightarrow5^x.\dfrac{19}{25}=2375\\ \Leftrightarrow5^x=3125\\ \Leftrightarrow5^x=5^5\\ \Leftrightarrow x=5\)

Answer 2

\(5^x-5^{x-1}-5^{x-2}=2375\)

\(\Rightarrow5^{x-2}\left(5^2-5^1-1\right)=2375\)

\(\Rightarrow5^{x-2}.19=2375\)

\(\Rightarrow5^{x-2}=125=5^3\Rightarrow x-2=3\Rightarrow x=5\)