|log[a] x| = log[a^2] x + 1
log[a] x = log[a^2] x + 1 (Eq. 1) or log[a] x = -log[a^2] x - 1 (Eq. 2)
Eq. 1:
(log x)/(log a) = (log x)/(log a^2) + 1
(log x)/(log a) = (log x)/(2log a) + 1
2log x = log x + 2log a
log x = 2log a
log x = log a^2
x = a^2
Eq. 2:
log[a] x = -log[a^2] x - 1
(log x)/(log a) = -(log x)/(log a^2) - 1
(log x)/(log a) = -(log x)/(2log a) - 1
2log x = -log x - 2log a
3log x = -2log a
log x^3 = log a^(-2)
x^3 = a^(-2)
x = a^(-2/3)
x = 1/a^(2/3)
Answers:
x = a^2 or x = 1/a^(2/3)
