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Given that log_{4n} (40*sqrt(3)) = log_{2n} (45), find n^3.

 Jul 2, 2022
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set log4n403–√=log3n45=tlog4n⁡403=log3n⁡45=t, thus

{4tnt=403–√3tnt=45{4tnt=4033tnt=45

we have

(43)t=83–√9=833–√⟹t=32(43)t=839=833⟹t=32

finally

8n32=403–√8n32=403

then

n3=75

 Jul 2, 2022

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