solve the logarithmic equation. be sure to reject any value of x that is not in the domain of the original logarithmic expression. give an exact answer. then, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

$\ln \sqrt{x+1} = 1$

rewrite the given equation without logarithms. do not solve for x.

Question

solve the logarithmic equation. be sure to reject any value of x that is not in the domain of the original logarithmic expression. give an exact answer. then, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

\$\ln \sqrt{x+1} = 1\$

rewrite the given equation without logarithms. do not solve for x.

$\ln \sqrt{x+1} = 1$

rewrite the given equation without logarithms. do not solve for x.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Equations" ], "new_concepts": [], "current_concepts": [ "Logarithmic Equations", "Logarithmic Properties" ] } ## Convert the logarithmic equation to exponential form $$ \begin{aligned} &\ln\sqrt{x+1} = 1 \ &\log_{e}\sqrt{x+1} = 1 \ &\sqrt{x+1} = e^1 \ &\sqrt{x+1} = e \end{aligned} $$ Rewrite the given equation without logarithms. Do not solve for x. $\sqrt{x+1} = e$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic Equations" ] }

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Explanation:

Convert the logarithmic equation to exponential form

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