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Recent questions tagged logarithms

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1 1 answer
284
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GATE ECE 2026 | GA | Question: 4
Real numbers $y, p$, and $n$ (all greater than $1$ ) satisfy\[\left(\log _{p^{1 / n}} y\right)\left(\log _{y^{1 / n}} p\right)=16\]where the logarithms are taken to the b...
8 8 votes
4 4 answers
2.4k
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GATE ECE 2024 | GA | Question: 4
​​​​For a real number $x>1$,$$\frac{1}{\log _{2} x}+\frac{1}{\log _{3} x}+\frac{1}{\log _{4} x}=1$$ The value of $x$ is$4$$12$$24$$36$
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1 1 vote
0 0 answers
445
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TIFR ECE 2015 | Question: 11
For $x>0$, for which range of values of $\alpha$ is the following inequality true?\[x \log _{e}(x) \geq x-\alpha\]$\alpha \geq 1 / 2$$\alpha \geq 0$$\alpha \leq 2$$\alpha...
14 14 votes
1 answers 1 answer
735
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GATE ECE 2015 Set 3 | GA | Question: 9
$\log \tan1^{\circ}+ \log \tan2^{\circ}+ \dots + \log \tan89^{\circ}$ is$1$$\frac{1}{\sqrt{2}}$$0$$-1$
10 10 votes
2 answers 2 answers
617
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GATE ECE 2015 Set 1 | GA | Question: 5
If $\log_{x}{(\frac{5}{7})}=\frac{-1}{3},$ then the value of $x$ is$343/125$$125/343$$-25/49$$-49/25$
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