Question

Resolva as equações exponenciais: a) 3 x = 81 b) 4 x−1 = 64 c) 3 x−2 = 9

Answer 1

Explicação passo-a-passo:

81= 3 × 3 × 3 × 3= 3^4

64= 2 × 2 × 2 × 2 × 2 × 2= 2^6

9= 3 × 3= 3²

a)

${3}^{x} = 81 = > { {3}^{x} } = {3}^{4} = > x = 4$

b)

${4}^{x - 1} = 64 = >( {2}^{2} ) {}^{x - 1 } = {2}^{6 } = > {2}^{2x - 2} = {2}^{6} = > 2x - 2 = 6 = > 2x = 6 + 2 = > 2x = 8 = > x = \frac{8}{2} = > x = 4$

${3}^{x - 2} = 9 = > {3}^{x - 2} = {3}^{2} = > x - 2 = 2 = > x = 2 + 2 = > x = 4$