Question

5^x-2+5^x-3+5^x-4=775

Answer 1

[tex]5^{x-2}+5^{x-3}+5^{x-4}=775\\ 5^x \cdot \frac{1}{5^2}+5^x \cdot \frac{1}{5^3}+5^x\cdot \frac{1}{5^4}=775|\cdot 5^4\\ 5^2\cdot5^x+5\cdot5^x+5^x=775 \cdot 625 \\ 25\cdot5^x+5\cdot5^x+5^x=484375\\ 31\cdot 5^x=484375\\ 5^x=15625\\ 5^x=5^6 \Rightarrow \boxed{\boxed{x=6}}[/tex]