st","extracted_subject":"MATH","extracted_chapter":"DIFFRENTIATION AND APPLICATIONS OF DERIVATIVES","extracted_topic":"DIFFERENTIATION BY SUBSTITUTION, HIGHER ORDER DERIVATIVES","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1631.png?top_left_x=532&top_left_y=1168&width=532&height=246&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e6f425d76b7ab31c3c2","slug":"the-solution-set-of-x-gx-where-x-12-5sup2x-1sup-an","content":"The solution set of ′(x) \\> g′(x) where (x) = (1/2) 5^{2x + 1} and g(x) = 5^x + 4x log_e 5 is –","options":[{"_id":"68a39e357f15af4716bbf5df","text":"(1, ∞)","sequence":0,"isCorrect":false},{"_id":"68a39e357f15af4716bbf5e0","text":"(0, 1)","sequence":1,"isCorrect":false},{"_id":"68a39e357f15af4716bbf5e1","text":"\\[0, ∞)","sequence":2,"isCorrect":false},{"_id":"68a39e357f15af4716bbf5e2","text":"(0, ∞)","sequence":3,"isCorrect":true}],"correct_answer":"(0, ∞)","explanation":"\\(\\left( \\frac{1}{2} \\right)\\)5^{2x + 1} log_e5 × 2 \\> 5^x log_e 5 + 4 log_e 5\n\n⇒ 5^2x . 5 \\> 5^x + 4\n\n⇒ 5 . 5^2x – 5^x – 4 \\> 0\n\n⇒ (5^x – 1) (5.5^x + 4) \\> 0 Q 5^x \\> 1\n\n∴ x \\> 0.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:35.465Z","__v":0,"vector_store_id":"731d6d5c-a579-4b27-8b29-d0777359a286","updated_at":"2024-08-30T21:49:35.465Z","isStarred":false},"params":{"questionSlug":"the-solution-set-of-x-gx-where-x-12-5sup2x-1sup-an"}}]}]]

Question: The solution set of ′(x) \> g′(x) where (x) = (1/2) 5<sup>2x + 1</sup> and g(x) = 5<sup>x</sup> + ...

Solution

Question: The solution set of ′(x) \> g′(x) where (x) = (1/2) 5<sup>2x + 1</sup> and g(x) = 5<sup>x</sup> + ...