Logarithms - Algebra - Mathematics Previous Year Questions

If x satisfies the inequality \({\log _{25}}{x^2} + {({\log _5}x)^2} < 2\), then x belongs to

If \(\left(x^2 \log _x 27\right) \cdot \log _9 x=x+4\) then the value of \(x\) is

The value of $(016)^{\log _{25}\left(\frac{1}{3}+\frac{1}{3^2}+\ldots+\infty\right)}$ is equal to

$..........$

The set of real value of $x$ for which $\log _{0.2} \frac{x+2}{x} \leq 1$ is

If \({\log _5}\,\,{\log _5}\,\,{\log _2}x = 0\) then value of x is

If x = log_abc, y = log_bca, z = log_cab, then the value of \({1 \over {1 + x}} + {1 \over {1 + y}} + {1 \over {1 + z}}\) will be

The value of \(\left( {{1 \over {{{\log }_3}12}} + {1 \over {{{\log }_4}12}}} \right)\) is

The value of \({{{{\log }_3}5 \times {{\log }_{25}}27 \times {{\log }_{49}}7} \over {{{\log }_{81}}3}}\) is

If \({\log _3}x + {\log _3}y = 2 + {\log _3}2\) and \({\log _3}(x + y) = 2\), then

If \({\log _7}2 = \lambda\), then the value of \({\log _{49}}(28)\) is

The sequence log a, \(\log {{{a^2}} \over b}\), \(\log {{{a^3}} \over {{b^2}}}\), ...... is

The sum of the series \({1 \over {1.2}} - {1 \over {2.3}} + {1 \over {3.4}} - \,\,.....\,\,\infty\) is