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

A. - 4

B. 4

C. 1 / 4

D. 10

DarkCalculis
Feb 16, 2018

#1**+1 **

Solve for x:

-log(8)/log(x) = -3/2

Take the reciprocal of both sides:

-log(x)/log(8) = -2/3

Multiply both sides by -log(8):

log(x) = (2 log(8))/3

(2 log(8))/3 = log(8^(2/3)) = log(4):

log(x) = log(4)

Cancel logarithms by taking exp of both sides:

**x = 4**

Guest Feb 16, 2018

#2**+1 **

Remember, DC, that

log a = b in exponential form is 10^b = a

So

Log_{x} (1 / 8) = - 3 / 2 =

x^(-3/2) = 1/8 take each side to the (-2/3) power

x = (1/8)^(-2/3) = [ (1/8)^(1/3) ]^(-2) = ( 1 / ^{3}√8 )^(-2) = (1/2)^(-2)

Note now that (1/a)^(-m) = a^m

So

(1/2)^(-2) = (2)^2 = 4 = x

CPhill
Feb 16, 2018