GATE EC 2026 Set 1 — Question 4
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33MediumRatios, Percentages, Powers, Exponents & LogarithmsQuantitative AptitudeGeneral Aptitude
General Aptitude → Quantitative Aptitude → Ratios, Percentages, Powers, Exponents & Logarithms
Last updated
Question
Real numbers , , and (all greater than 1) satisfy
,
where the logarithms are taken to the bases and .
The value of is ________.
,
where the logarithms are taken to the bases and .
The value of is ________.
Correct answer
(B) 4
Solution
Given the equation: We use the change of base formula for logarithms: .
Let's convert the given logarithms to a common base, say (natural logarithm).Substitute these back into the given equation:As and , and . Thus, and are reciprocals and their product is 1.Since is a real number and greater than 1, we take the positive square root:
Thus, the value of is 4.The final answer is
Let's convert the given logarithms to a common base, say (natural logarithm).Substitute these back into the given equation:As and , and . Thus, and are reciprocals and their product is 1.Since is a real number and greater than 1, we take the positive square root:
Thus, the value of is 4.The final answer is
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EC question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Quantitative Aptitude
2026 Set 1 Q1Among the following options, the antonym of the word ‘nocturnal’ is _________.2026 Set 1 Q2The statements (S1), (S2), and (S3) pertain to the scores obtained by students in an exam. The…2026 Set 1 Q3The figure below has exactly three intersecting line segments with a rectangular portion …2026 Set 1 Q5The following observation is made about the scores obtained by 100 students in an exam: 'For each…2026 Set 1 Q6Each one of the following clues contains a keyword that is partially filled. Clue 1: Synonym of…