Question

32 elevado a x-7=64 elevado a x-1

Answer 1

$32^{x-7} = 64^{x-1}$

Fatoramos os dois números:

32 | 2
16 | 2
  8 | 2
  4 | 2
  2 | 2
  1

32 = 2⁵

64 | 2
32 | 2
16 | 2
  8 | 2
  4 | 2
  2 | 2
  1

64 = 2⁶

$32^{x-7} = 64^{x-1} \\\\ (2^{5})^{x-7} = (2^{6})^{x-1} \\\\ 2^{5x-35} = 2^{6x-6} \\\\ \not 2^{5x-35} = \not 2^{6x-6} \\\\ 5x-35 = 6x-6 \\\\ 6x-5x = -35+6 \\\\ \boxed{\boxed{x = -29}}$