Question

Решите плез 8^(x-1)+8^(x-2)*6+33*7^(x-2)-7^x=0

Answer 1

$\displaystyle 8^{x-1}+8^{x-2}*6+33*7^{x-2}-7^x=0;\\\frac{8^x}{8}+\frac{6*8^x}{64}=7^x-\frac{33*7^x}{49};\\\frac{(4+3)*8^x}{32}=\frac{(49-33)7^x}{49};\\\frac{7*8^x}{32}=\frac{16*7^x}{49};\\7^38^x=8^37^x;\ :7^37^x;\\(\frac{8}{7})^x=(\frac{8}{7})^3;\\\boxed{x=3;}$