Question

If Logx (1 / 8) = - 3 / 2, then x is equal to

Answer 1

log (1/8)/log x =-3/2 ;now log is base 10.
therefore,
log (1/8) = -0.9030.
then
log x = -0.6020
find the anti-log and you have
x = 0.25

Answer 2

log_x (1/8) = -3/2
means:
x^(-3/2) = 1/8
x^(3/2) = 8
(√x)^3 = 8
√x = 2
x = 4

check:
log₄ (1/8)
= log₄1 - log₄8
= 0 - 3/2 , (since 4^(3/2) = 8)
= -3/2