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Category: Logarithms

what-is-2-log2x-3-log3x-

Question Number 103961 by MMpotulo last updated on 18/Jul/20 $${what}\:{is}\: \\ $$$$\mathrm{2}^{{log}\mathrm{2}{x}} =\mathrm{3}^{{log}\mathrm{3}{x}} \\ $$ Answered by bramlex last updated on 18/Jul/20 $$\mathrm{ln}\:\left(\mathrm{2}^{\mathrm{ln}\:\left(\mathrm{2}{x}\right)} \right)\:=\:\mathrm{ln}\:\left(\mathrm{3}^{\mathrm{ln}\:\left(\mathrm{3}{x}\right)} \right)…

log-3-x-2-2-lt-log-3-3-2-x-1-

Question Number 167243 by greogoury55 last updated on 10/Mar/22 $$\:\:\:\:\:\:\mathrm{log}\:_{\mathrm{3}} \left({x}^{\mathrm{2}} −\mathrm{2}\right)<\:\mathrm{log}\:_{\mathrm{3}} \left(\frac{\mathrm{3}}{\mathrm{2}}\mid{x}\mid−\mathrm{1}\right)\: \\ $$ Answered by MJS_new last updated on 10/Mar/22 $$\mathrm{lhs}=\mathrm{rhs}\:\Rightarrow\:{x}=\pm\mathrm{2};\:\mathrm{lhs}\:\mathrm{defined}\:\mathrm{for}\:\mid{x}\mid>\sqrt{\mathrm{2}} \\ $$$$\Rightarrow…

Question-167215

Question Number 167215 by Avijit007 last updated on 09/Mar/22 Answered by MikeH last updated on 09/Mar/22 $$\mathrm{log}_{{b}} {a}\:×\:\mathrm{log}_{{c}} {b}\:×\:\mathrm{log}_{{a}} {c}\:= \\ $$$$\:\frac{\mathrm{1}}{\cancel{\mathrm{log}_{{a}} {b}}}\:×\:\frac{\cancel{\mathrm{log}_{{a}} {b}}}{\mathrm{log}_{{a}} {c}}×\:\mathrm{log}_{{a}}…

solve-the-inequality-3-log-x-2-5x-1-3-log-x-2-3-3x-

Question Number 101553 by bobhans last updated on 03/Jul/20 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{inequality} \\ $$$$\left(\:^{\mathrm{3}} \mathrm{log}\:{x}+\mathrm{2}\right)^{\mathrm{5}{x}+\mathrm{1}} \:\geqslant\:\left(\:^{\mathrm{3}} \mathrm{log}\:{x}\:+\mathrm{2}\right)^{\mathrm{3}−\mathrm{3}{x}} \\ $$ Answered by bramlex last updated on 03/Jul/20 $$\rightarrow\left(\mathrm{log}\:_{\mathrm{3}}…

To-sir-Tinkutara-please-sir-can-you-help-us-with-a-development-which-allows-our-maths-work-which-is-saved-to-be-converted-directly-to-a-portable-document-format-PDF-

Question Number 101447 by Rio Michael last updated on 02/Jul/20 $$\mathrm{To}\:\mathrm{sir}\:\mathrm{Tinkutara}:\:\mathrm{please}\:\mathrm{sir}\:\mathrm{can}\:\mathrm{you}\:\mathrm{help}\:\mathrm{us} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{development}\:\mathrm{which}\:\mathrm{allows}\:\mathrm{our}\:\mathrm{maths}\:\mathrm{work} \\ $$$$\mathrm{which}\:\mathrm{is}\:\mathrm{saved}\:\mathrm{to}\:\mathrm{be}\:\mathrm{converted}\:\mathrm{directly}\:\mathrm{to}\:\mathrm{a}\: \\ $$$$\mathrm{portable}\:\mathrm{document}\:\mathrm{format}\left(\mathrm{PDF}\right)?\: \\ $$ Commented by Tinku Tara last updated…