Question

Решить уравнения :

а) $4^{x+1} + 2^{2x} = 80$

б) $2*3^{x} + 3^{x-1} = 57$

Answer 1

$a)\\4^{x+1}+2^{2x}=80\\4*4^x + 4^x = 80\\5*4^x = 80\\4^x = 16 = 4^2\\x = 2\\Answer: x = 2\\b)\\2*3^x+3^{x-1}=57 | *3\\6*3^x+3^x=171\\7*3^x=171\\3^x=\frac{171}{7}\\x = log_3\frac{171}{7}\\Answer: x = log_3\frac{171}{7}$