Mathematics

Maths related to High School Mathematics, Madhyamik Mathematics, Engineering Mathematics, and Graduation level Mathematics

Problem 0015 | Logarithm

Submitted by Publisher on Sun, 02/17/2013 - 22:05

উদাহরণ ১৫৷[tex]\frac{{\log x}}{{ry - qz}} = \frac{{\log y}}{{pz - rx}} = \frac{{\log z}}{{qx - py}}[/tex]  হলে দেখাও যে  [tex]{x^p}{y^q}{z^r} = 1[/tex]                       [H.S ‘92]

সমাধান:

Problem 0014 | Logarithm

Submitted by Publisher on Sun, 02/17/2013 - 21:49

উদাহরণ ১৪৷ [tex]{a^4} + {b^4} = 14{a^2}{b^2}[/tex]  হলে দেখাও যে

  [tex]{\log _e}\left( {{a^2} + {b^2}} \right) = {\log _e}a + {\log _e}b + {\log _e}2[/tex]                                                    [H.S ‘88]

প্রমান:

Problem 009 | Logarithm

Submitted by Publisher on Sun, 02/17/2013 - 21:00

উদাহরণ ৯৷[tex]a > 0,c > b = \sqrt {ac} ,a,c,ac \ne 1,N > 0[/tex]  হলে প্রমান করো

  [tex]\frac{{{{\log }_a}N}}{{{{\log }_c}N}} = \frac{{{{\log }_a}N - {{\log }_b}N}}{{{{\log }_b}N - {{\log }_c}N}}[/tex]                                             [Jt.Ent.’88]

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Problem 006 | Logarithm

Submitted by Publisher on Sun, 02/17/2013 - 20:24

উদাহরণ ৬৷ দেখাও যে [tex]{\log _{10}}2[/tex] এর মান [tex]\frac{1}{3}[/tex] এবং [tex]\frac{1}{4}[/tex] এর মধ্যে থাকে।                   [H.S’2000]

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