If log(x) 1/8 = -3/2, what is x >

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hala718 eNotes educator | Certified Educator

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Given that log(x) 1/8 = -3/2

We need to find x value.

First we will rewrite the fraction (1/8)

==> We know that 1/8 = (1/2)^3 = 1/2^3 = 2^-3

We will substitute.

==> log(x) 2^-3 = -3/2

Now we know that log a^b = b*log a

==> -3*logx 2 = -3/2

We will divide by -3.

==> logx 2 = 1/2

Now we will rewrite into the exponent form.

=> x^1/2 = 2

Now we will square both sides.

==> x = 4

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justaguide eNotes educator | Certified Educator

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We have to find x from log(x) 1/8 = -3/2

log(x) 1/8 = -3/2

=> log (x) 8^-1 = -3/2

=> log (x) 4^(-3/2) = -3/2

take the antilog of both the sides

=> 4^(-3/2) = x^(-3/2)

as the exponent is the same, we can equate the base

=> x = 4

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