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

log_(9)x=-(1)/(2)
Answer:

Solve the following logarithm problem for the positive solution for $x$ . $\newline$ $\log _{9} x=-\frac{1}{2}$ $\newline$ 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 _{9} x=-\frac{1}{2}

\newline

Answer:

Understand the equation: Understand the logarithmic equation. $\newline$ We have the equation $\log_9(x) = -(\frac{1}{2})$ . This means we are looking for a number $x$ such that when $9$ is raised to the power of $-(\frac{1}{2})$ , we get $x$ .
Convert to exponential form: Convert the logarithmic form to exponential form. $\newline$ Using the definition of a logarithm, we can rewrite the equation in its exponential form: $9^{-(1/2)} = x$ .
Calculate $9^{(-1/2)}$ : Calculate $9$ raised to the power of $-(1/2)$ . $\newline$ The exponent $-(1/2)$ means we need to take the square root of $9$ and then take the reciprocal of that result. The square root of $9$ is $3$ , so the reciprocal of $3$ is $1/3$ . Therefore, $9^{(-(1/2))} = 1/3$ .
Write down the solution: Write down the solution. $\newline$ Since $9^{-(1/2)} = \frac{1}{3}$ , we have found that $x = \frac{1}{3}$ .

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