select all of the potential solution(s) of the equation $2\log_{5}x = \log_{5}4$.

$x = -2$
$x = 4$
$x = 16$
$x = -10$
$x = 2$

what is the solution to $2\log_{5}x = \log_{5}4$?

$x = $

Question

select all of the potential solution(s) of the equation $2\log_{5}x = \log_{5}4$.

$x = -2$
$x = 4$
$x = 16$
$x = -10$
$x = 2$

what is the solution to $2\log_{5}x = \log_{5}4$?

$x = $

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Power Rule", "Solving Logarithmic Equations", "Domain of Logarithmic Functions" ], "new_concepts": [], "current_concepts": [ "Logarithmic Power Rule", "Solving Logarithmic Equations", "Domain of Logarithmic Functions", "Extraneous Solutions" ] } ## Apply the logarithmic power rule Using the *Logarithmic Power Rule* knowledge point $$ \begin{aligned} 2\log_{5}x &= \log_{5}(x^2) \ \log_{5}(x^2) &= \log_{5}4 \end{aligned} $$ ## Solve the algebraic equation Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} x^2 &= 4 \ x &= \pm 2 \end{aligned} $$ ## Check the domain constraints Using the *Domain of Logarithmic Functions* knowledge point $$ \begin{aligned} &\text{For } \log_{5}x \text{ to be defined, } x > 0. \ &x = -2 \text{ is extraneous.} \ &x = 2 \text{ is the only valid solution.} \end{aligned} $$ ## Question 1 The potential solutions (algebraic solutions before checking the domain constraint) are: * $x = -2$ * $x = 2$ ## Question 2 The actual solution to the equation is: $x =$ 2 { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Solving Logarithmic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the logarithmic power rule

Solve the algebraic equation

Check the domain constraints

Answer:

Question 1

Question 2