Question

5. Resolva as equações exponenciais:
a)3x-2=9
e)7 3x+1=49
c)5x-1 = 125
d) 7x-3 = 49
b) 2x+5 = 16
f) 10 2x-5 = 100000​

Answer 1

Explicação passo-a-passo:

a)

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

b)

${7}^{3x + 1} = 49 = > {7}^{3x + 1} = {7}^{2} = > 3x + 1 = 2 = > 3x = 2 - 1 = > 3x = 1 = > x = \frac{1}{3}$

c)

${5}^{x - 1} = 125 = > {5}^{x - 1} = {5}^{3} = > x - 1 = 3 = > x = 3 + 1 = > x = 4$

d)

${7}^{x - 3} = 49 = > {7}^{x - 3} = {7}^{2} = > x - 3 = 2 = > x = 2 + 3 = > x = 5$

b)

${2}^{x + 5} = 16 = > {2}^{x + 5} = {2}^{4} = > x + 5 = 4 = > x = 4 - 5 = > x = - 1$

f)

${10}^{2x - 5} = 100000 = > {10}^{2x - 5} = {10}^{5} = > 2x - 5 = 5 = > 2x = 5 + 5 = > 2x = 10 = > x = \frac{10}{2} = > x = 5$