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Author: Tinku Tara

f-x-f-x-f-x-

Question Number 4817 by 123456 last updated on 15/Mar/16 $${f}\left(\alpha{x}\right)=\alpha{f}\left({x}−\alpha\right) \\ $$$${f}\left({x}\right)=? \\ $$ Commented by prakash jain last updated on 15/Mar/16 $${x}=\mathrm{0} \\ $$$$\mathrm{Trivial}\:\mathrm{solution}\:\mathrm{satisfies}\:\mathrm{the}\:\mathrm{equation}\:{f}\left({x}\right)=\mathrm{0}…

Question-4816

Question Number 4816 by Kelvin last updated on 15/Mar/16 Commented by prakash jain last updated on 15/Mar/16 $$\mathrm{log}\:.\mathrm{006}−\mathrm{log}\:.\mathrm{0012}=\mathrm{log}\:\frac{.\mathrm{006}}{.\mathrm{0012}}=\mathrm{log}\:\frac{\mathrm{60}}{\mathrm{12}}=\mathrm{log}\:\mathrm{5} \\ $$$$\mathrm{log}\:.\mathrm{007}−\mathrm{log}\:.\mathrm{00243}=\mathrm{log}\:\frac{.\mathrm{007}}{.\mathrm{00243}}=\mathrm{log}\:\frac{\mathrm{700}}{\mathrm{243}} \\ $$$$\mathrm{log}\:.\mathrm{008}+\mathrm{log}\:\mathrm{4000}=\mathrm{log}\:\left(.\mathrm{008}×\mathrm{4000}\right)=\mathrm{log}\:\mathrm{32}=\mathrm{5log}\:\mathrm{2} \\ $$$$\mathrm{log}\:.\mathrm{0128}=\mathrm{7log}\:\mathrm{2}−\mathrm{log}\:\mathrm{10000}=\mathrm{7log}\:\mathrm{2}−\mathrm{4} \\…

n-1-H-n-7-n-2-H-n-7-n-1-2-k-1-n-1-k-m-H-n-m-

Question Number 135884 by Dwaipayan Shikari last updated on 16/Mar/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} ^{\left(\mathrm{7}\right)} }{{n}^{\mathrm{2}} }−\frac{{H}_{{n}} ^{\left(\mathrm{7}\right)} }{\left({n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}^{{m}} }={H}_{{n}} ^{\left({m}\right)}…