JEE MAIN Logarithms And Indices Previous Year Questions (PYQs) – Page 1 of 2
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If $\log_e a,\ \log_e b,\ \log_e c$ are in an A.P. and
$\log_e a-\log_e 2b,\ \log_e 2b-\log_e 3c,\ \log_e 3c-\log_e a$ are also in an A.P.,
then $a:b:c$ is equal to:
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Solution
If for x $\in$ $\left( {0,{\pi \over 2}} \right)$, log10sinx + log10cosx = $-$1 and log10(sinx + cosx) = ${1 \over 2}$(log10 n $-$ 1), n > 0, then the value of n is equal to :
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Solution
For three positive integers $p, q, r$, $x^{p q^{2}} = y^{q r} = z^{p^{2} r}$ and $r = pq + 1$ such that
$3,\ 3\log_{y}x,\ 3\log_{z}y,\ 7\log_{x}z$ are in A.P. with common difference $\dfrac{1}{2}$.
Then $r - p - q$ is equal to:
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Solution
The number of integral solutions $x$ of $\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^{2} \geq 0$ is :
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Solution
The sum of all the solutions of the equation $(8)^{2x}-16\cdot(8)^x+48=0$ is:
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Solution
Let $y=\log_e!\left(\dfrac{1-x^2}{1+x^2}\right)$, with $-1
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Solution
If $\log_e a,;\log_e b,;\log_e c$ are in an A.P. and
$\log_e a-\log_e(2b),;\log_e(2b)-\log_e(3c),;\log_e(3c)-\log_e a$ are also in an A.P., then $a:b:c$ is equal to:
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Solution
The sum of all real values of $x$ satisfying the equation
$2^{(x-1)(x^{2} + 5x - 50)} = 1$ is:
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Solution
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