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Solve the following logarithm problem for the positive solution for
x.

log_(x)((1)/(8))=-(3)/(4)
Answer:

Solve the following logarithm problem for the positive solution for $x$ . $\newline$ $\log _{x} \frac{1}{8}=-\frac{3}{4}$ $\newline$ Answer:

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Quotient property of logarithms

Full solution

Q. Solve the following logarithm problem for the positive solution for

x

.

\newline

\log _{x} \frac{1}{8}=-\frac{3}{4}

\newline

Answer:

Understand logarithmic equation: Understand the logarithmic equation. $\newline$ The given logarithmic equation is $\log_{x} \frac{1}{8} = -\frac{3}{4}$ . This means that $x$ raised to the power of $-\frac{3}{4}$ equals $\frac{1}{8}$ . $\newline$ Mathematically, this can be written as $x^{-\frac{3}{4}} = \frac{1}{8}$ .
Convert to exponential form: Convert the logarithmic equation to exponential form. $\newline$ Using the definition of a logarithm, we can rewrite the equation in its exponential form: $x^{(-3/4)} = \frac{1}{8}$ .
Recognize power of $1/8$ : Recognize that $1/8$ is a power of $2$ . $\newline$ Since $1/8$ is $2^{-3}$ , we can rewrite the equation as $x^{-3/4} = 2^{-3}$ .
Set exponents equal: Set the exponents equal to each other. $\newline$ Since the bases are equal $x$ and $2$ , we can set the exponents equal to each other: $-\frac{3}{4} = -3$ .

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