test","extracted_subject":"MATH","extracted_chapter":"LOGARITHM, INDICES SURDS, PARTIAL FRACTION (OUT OF SYLLABUS)","extracted_topic":"LOGARITHMS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2037.png?top_left_x=0&top_left_y=1186&width=532&height=259&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e73425d76b7ab31faad","slug":"the-least-value-of-the-expression-2logsub10subx-lo","content":"The least value of the expression\n\n2log₁₀x – log_x(0.01), for x \\> 1, is-","options":[{"_id":"68a374637f15af4716b4dda7","text":"10","sequence":0,"isCorrect":false},{"_id":"68a374637f15af4716b4dda8","text":"2","sequence":1,"isCorrect":false},{"_id":"68a374637f15af4716b4dda9","text":"–0.01","sequence":2,"isCorrect":false},{"_id":"68a374637f15af4716b4ddaa","text":"None of these","sequence":3,"isCorrect":true}],"correct_answer":"None of these","explanation":"log_x.01 = –2 log_x10\n\nThus expression = 2 [log₁₀x + log_x10]\n\n= 2 \\(\\left\\lbrack \\log_{10}x + \\frac{1}{\\log_{10}x} \\right\\rbrack\\)\n\nPut log₁₀x = 1\n\nBut x + \\(\\frac{1}{x}\\) ³ 2 if x \\> 0 and x + \\(\\frac{1}{x}\\) £ –2 if x \\< 0 least value of\n\nexpression = 4 because\n\nlog₁₀x \\< 0 \" x \\> 1\n\nSo correct choice is","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:39.011Z","__v":0,"vector_store_id":"6c292534-f79c-489d-9e71-dd71bfa76887","updated_at":"2024-08-30T21:49:39.011Z","isStarred":false},"params":{"questionSlug":"the-least-value-of-the-expression-2logsub10subx-lo"}}]}]]

Question: The least value of the expression 2log<sub>10</sub>x – log<sub>x</sub>(0.01), for x \> 1, is-...

Solution