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Question-221814

Question Number 221814 by Tawa11 last updated on 10/Jun/25 Answered by wewji12 last updated on 11/Jun/25 $$\mathrm{log}_{{a}} \left({b}\right)=\frac{\mathrm{log}_{{b}} \left({c}\right)}{\mathrm{log}_{{a}} \left({c}\right)} \\ $$$$\frac{\mathrm{ln}\left(\mathrm{2}\right)}{\mathrm{ln}\left({x}+\mathrm{1}\right)}+\frac{\mathrm{ln}\left(\mathrm{3}\right)}{\mathrm{ln}\left({x}+\mathrm{2}\right)}+\frac{\mathrm{ln}\left(\mathrm{4}\right)}{\mathrm{ln}\left({x}+\mathrm{3}\right)}=\mathrm{3} \\ $$$$\mathrm{if}\:{x}=\mathrm{1}\: \\…

n-1-m-1-1-m-2-n-2-2-

Question Number 221228 by Nicholas666 last updated on 27/May/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\underset{{m}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left({m}^{\mathrm{2}} \:+\:{n}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$ \\ $$ Answered by…