If 1-log3 - - 1-log4 - - x- then x be

1/log_3 π + 1/log_4 π gt; x ⇒ log_π 3 + log_π 4 gt; x ⇒ log_π 12 gt; x We know, π^2 lt; 12 lt; π^3 ∴ 12 gt; π^2 ; ∴ log_π 12 gt; log_ππ^2 i. ...

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Logarithmic Inequalities

If 1/log3 π +...

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If $\frac{1}{l o g_{3} π} + \frac{1}{l o g_{4} π} > x$ , then x be

2

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3

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3.5

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π

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p = \frac{1}{{log}_{3} π} + \frac{1}{{log}_{4} π} + 1

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{log}_{3} (\sqrt{5 x - 2}) - \frac{1}{2} = {log}_{3} (\sqrt{x + 4})

{log}_{2} x, {log}_{3} x, {log}_{e} x, {log}_{4} x

x > 1

0 < x < 1

A = \frac{1}{π} ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} {sin}^{- 1} (π x) & {tan}^{- 1} (\frac{π}{x}) {sin}^{- 1} (\frac{π}{x}) & {tan}^{- 1} (π x) \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦, B = \frac{1}{π} ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} - {cos}^{- 1} (π x) & {tan}^{- 1} (\frac{π}{x}) {sin}^{- 1} (\frac{π}{x}) & - {tan}^{- 1} (π x) \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

A - B

If $(3 x)^{l o g 3} = (4 y)^{l o g 4}$ and $(4)^{l o g x} = (3)^{l o g y}$ , then x equals

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