Question

If Logx (1 / 8) = - 3 / 2, then x is equal to
a. - 4
b. 4
c. 1 / 4
d. 10

Answer 1

`log_x (1)/(8) = -(3)/(2) \\\\ which\ is \ the \is \ the \ same \ thing\ as \ saying\ \\\\x^ {-(3)/(2) }= (1)/(8) \\\\x^ {-(3)/(2) }= (1)/(2^3) \\\\x^ {-(3)/(2) }= 2^(-3) \\\\ x^ {-(3)/(2) }= 2^{-3*2* (1)/(2) } \\\\ x^ {-(3)/(2) }= ((2)^2)^{-3* (1)/(2) } \\\\ x^ {-(3)/(2) }= 4^{-(3)/(2) }`

Now,

Since the "x" and the "4" have the same exponent and they equal eachother,
x = 4