Question

1 - Resolva as equações: a) log½ (log9 x) = 1 b) log3 ( 2x - 1) = 4

Answer 1

Item a)

log_1/2 (log_9 (x)) = 1

log_9 (x) = (1/2)^1

log_9 (x) = 1/2

x = 9^(1/2)

x = (3^2)^(1/2)

x = 3^(2/2)

x = 3^1

x = 3

Item b)

log_3 (2x - 1) = 4

2x - 1 = 3^4

2x - 1 = 81

2x = 81 + 1

2x = 82

x = 82/2

x = 41

Obs.: foi aplicado a definição de logaritmo... log_a (b) = c <=> b = a^c