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Logarithm

8 questions · Mathematics · JEE Main

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JEE Main
Mathematics
Logarithm

Logarithm

8 questions · Mathematics · JEE Main

The product of all solutions of the equation $e^{5 (l o g_{e} x)^{2} + 3} = x^{8}, x > 0$ , is :2025 · 22 Jan · Shift 1 · Q31 · MCQ
Let a, b, c be three distinct positive real numbers such that $(2 a)^{l o g_{e} a} = (b c)^{l o g_{e} b}$ and $b^{l o g_{e} 2} = a^{l o g_{e} c}$ . Then, 6a + 5bc is equal to .2023 · 10 Apr · Shift 1 · Q46 · Numerical
The number of integral solutions $x$ of $lo g_{(x + \frac{7}{2})} (\frac{x - 7}{2 x - 3})^{2} \geq 0$ is :2023 · 11 Apr · Shift 1 · Q39 · MCQ
Let $S = {α : lo g_{2} (9^{2 α - 4} + 13) - lo g_{2} (\frac{5}{2} . 3^{2 α - 4} + 1) = 2}$ . Then the maximum value of $β$ for which the equation $x^{2} - 2 (α \in s \sum α)^{2} x + α \in s \sum (α + 1)^{2} β = 0$ …2023 · 25 Jan · Shift 1 · Q43 · Numerical
If the solution of the equation $lo g_{c o s x} cot x + 4 lo g_{s i n x} tan x = 1, x \in (0, \frac{π}{2})$ , is $sin^{- 1} (\frac{α + β}{2})$ , where $α$ , $β$ are integers, then $α + β$ …2023 · 30 Jan · Shift 1 · Q29 · MCQ
The number of solutions of the equation $lo g_{(x + 1)} (2 x^{2} + 7 x + 5) + lo g_{(2 x + 5)} (x + 1)^{2} - 4 = 0$ , x > 0, is :2021 · 20 Jul · Shift 2 · Q39 · Numerical
The number of solutions of the equation log4(x $-$ 1) = log2(x $-$ 3) is .2021 · 26 Feb · Shift 1 · Q38 · Numerical
The number of distinct solutions of the equation $lo g_{\frac{1}{2}} ∣ sin x ∣ = 2 - lo g_{\frac{1}{2}} ∣ cos x ∣$ in the interval [0, 2 $π$ ], is .2020 · 9 Jan · Shift 1 · Q34 · Numerical