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

log_(2)x=-5
Answer:

Solve the following logarithm problem for the positive solution for $x$ . $\newline$ $\log _{2} x=-5$ $\newline$ Answer:

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Product property of logarithms

Full solution

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

x

.

\newline

\log _{2} x=-5

\newline

Answer:

Understand Problem: Understand the problem and the logarithmic equation. $\newline$ We need to find the value of $x$ such that $\log_2(x) = -5$ . This means we are looking for the number $x$ that, when $2$ is raised to the power of $-5$ , equals $x$ .
Convert to Exponential: Convert the logarithmic equation to an exponential equation. $\newline$ Using the definition of a logarithm, we can rewrite the equation $\log_2(x) = -5$ as an exponential equation: $2^{-5} = x$ .
Calculate Value: Calculate the value of $2$ raised to the power of $-5$ . $2^{-5}$ is the same as $1/(2^5)$ . Since $2^5 = 32$ , we have $1/32$ as the value for $x$ .
Verify Solution: Verify that the solution is positive. $\newline$ Since $\frac{1}{32}$ is a positive number, we have found the positive solution for $x$ .

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