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Question Number 91862 by jagoll last updated on 03/May/20

log_2 (x)+log_3 (x) = 1 x =?

$$\mathrm{log}_{\mathrm{2}} \left({x}\right)+\mathrm{log}_{\mathrm{3}} \left({x}\right)\:=\:\mathrm{1} \\ $$$${x}\:=? \\ $$

Commented by Tony Lin last updated on 03/May/20

((lnx)/(ln2))+((lnx)/(ln3))=1 lnx(((ln6)/(ln2×ln3)))=1 lnx=((ln2×ln3)/(ln6)) x=e^((ln2×ln3)/(ln6)) ≈1.53

$$\frac{{lnx}}{{ln}\mathrm{2}}+\frac{{lnx}}{{ln}\mathrm{3}}=\mathrm{1} \\ $$$${lnx}\left(\frac{{ln}\mathrm{6}}{{ln}\mathrm{2}×{ln}\mathrm{3}}\right)=\mathrm{1} \\ $$$${lnx}=\frac{{ln}\mathrm{2}×{ln}\mathrm{3}}{{ln}\mathrm{6}} \\ $$$${x}={e}^{\frac{{ln}\mathrm{2}×{ln}\mathrm{3}}{{ln}\mathrm{6}}} \approx\mathrm{1}.\mathrm{53} \\ $$

Commented by jagoll last updated on 03/May/20

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Commented by hmamarques1994@gmail.com last updated on 03/May/20

x = 2^(log_6 3) ≈ 1,52959

$$\: \\ $$$$\:{x}\:=\:\mathrm{2}^{{log}_{\mathrm{6}} \:\mathrm{3}} \:\approx\:\mathrm{1},\mathrm{52959} \\ $$

Commented by john santu last updated on 03/May/20

2^(log_6 (3)) = 3^(log_6 (2))

$$\mathrm{2}^{\mathrm{log}_{\mathrm{6}} \left(\mathrm{3}\right)} \:=\:\mathrm{3}^{\mathrm{log}_{\mathrm{6}} \left(\mathrm{2}\right)} \\ $$

Answered by john santu last updated on 03/May/20

Commented by john santu last updated on 03/May/20

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Commented by john santu last updated on 03/May/20

1.52959232849

Commented by hmamarques1994@gmail.com last updated on 03/May/20

Ge^� nio!

$${G}\hat {{e}nio}! \\ $$

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