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




Question Number 86515 by jagoll last updated on 29/Mar/20
log_2  (x) + log_3  (x) = 1   x =
$$\mathrm{log}_{\mathrm{2}} \:\left(\mathrm{x}\right)\:+\:\mathrm{log}_{\mathrm{3}} \:\left(\mathrm{x}\right)\:=\:\mathrm{1}\: \\ $$$$\mathrm{x}\:=\: \\ $$
Commented by john santu last updated on 29/Mar/20
⇒ ^2 log x = ^2 log 3 .^3 log x   ⇔ ^3 log (x) { ^2 log 3 +1 } = 1  ^3 log x = (1/(^2 log 6)) =^6 log 2  x = 3^(^6 log 2)
$$\Rightarrow\:\:^{\mathrm{2}} \mathrm{log}\:\mathrm{x}\:=\:\:^{\mathrm{2}} \mathrm{log}\:\mathrm{3}\:.\:^{\mathrm{3}} \mathrm{log}\:\mathrm{x}\: \\ $$$$\Leftrightarrow\:\:^{\mathrm{3}} \mathrm{log}\:\left(\mathrm{x}\right)\:\left\{\:\:^{\mathrm{2}} \mathrm{log}\:\mathrm{3}\:+\mathrm{1}\:\right\}\:=\:\mathrm{1} \\ $$$$\:^{\mathrm{3}} \mathrm{log}\:\mathrm{x}\:=\:\frac{\mathrm{1}}{\:^{\mathrm{2}} \mathrm{log}\:\mathrm{6}}\:=\:^{\mathrm{6}} \mathrm{log}\:\mathrm{2} \\ $$$$\mathrm{x}\:=\:\mathrm{3}^{\:^{\mathrm{6}} \mathrm{log}\:\mathrm{2}} \\ $$
Commented by jagoll last updated on 29/Mar/20
thank you
$$\mathrm{thank}\:\mathrm{you} \\ $$

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