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Solve for a positive value of
x.

log_(x)(4)=2
Answer:

Solve for a positive value of $x$ . $\newline$ $\log _{x}(4)=2$ $\newline$ Answer:

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Product property of logarithms

Full solution

Q. Solve for a positive value of

x

.

\newline

\log _{x}(4)=2

\newline

Answer:

Understand Equation: Understand the given logarithmic equation. $\newline$ The equation $\log_{x}(4) = 2$ means that $x$ raised to the power of $2$ equals $4$ .
Convert to Exponential Form: Convert the logarithmic equation to its exponential form. $\newline$ Using the definition of a logarithm, we can rewrite the equation as $x^2 = 4$ .
Solve for x: Solve the exponential equation for x. $\newline$ To find $x$ , we take the square root of both sides of the equation. The square root of $4$ is $2$ , so $x = 2$ .
Check Restrictions: Check for any restrictions and whether the solution is positive. $\newline$ Since we are looking for a positive value of $x$ and $2$ is positive, our solution meets the criteria.

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