# What is x if log(x) (1/8) = -3/2.

Posted on

We have log(x) (1/8) = -3/2. We have to determine x.

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

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

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

=> (1/4)^(3/2) = x^(-3/2)

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

As the exponent are equal we can equate the base.

=> x = 4

The required value of x is x = 4.

Posted on

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

We need to find the values of x.

==> Let us simplify.

First we will rewrite (1/8) = (1/2)^3

==> (1/2)^3 = 2^-3

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

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

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

We will divide by -3.

==> log(x) 2 = -3/2*-3 = 1/2

Now we will rewrite using exponent form.

==> x^1/2 = 2

We will square both sides.

==> x = 4
The text passage contains a mathematical question and its solution, presented in two different posts. Both posts solve the same logarithmic equation to find the value of x.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# What is x if log(x) (1/8) = -3/2.

Posted on

We have log(x) (1/8) = -3/2. We have to determine x.

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

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

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

=> (1/4)^(3/2) = x^(-3/2)

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

As the exponent are equal we can equate the base.

=> x = 4

The required value of x is x = 4.

Posted on

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

We need to find the values of x.

==> Let us simplify.

First we will rewrite (1/8) = (1/2)^3

==> (1/2)^3 = 2^-3

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

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

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

We will divide by -3.

==> log(x) 2 = -3/2*-3 = 1/2

Now we will rewrite using exponent form.

==> x^1/2 = 2

We will square both sides.

==> x = 4
user
The text passage contains a mathematical question and its solution, presented in two different posts. Both posts solve the same logarithmic equation to find the value of x.

TYPE: SINGLE_QUESTION_WITH_ANSWER