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Question Number 190395 by mr W last updated on 02/Apr/23

which is larger,  2^(234)  or 5^(100)  ?

whichislarger,2234or5100?

Answered by aba last updated on 02/Apr/23

2^(234) >5^(100)

2234>5100

Commented by Frix last updated on 02/Apr/23

Prove it?

Proveit?

Answered by nikif99 last updated on 02/Apr/23

234 log 2≶100 log 5=100(log (((10)/2)))=  100(log 10−log 2)=100−100 log 2 ⇒  234 log 2≶100−100 log 2 ⇒  334 log 2≶100 ⇒334×0.30103>100

234log2100log5=100(log(102))=100(log10log2)=100100log2234log2100100log2334log2100334×0.30103>100

Commented by Frix last updated on 02/Apr/23

Prove must be without calculation.  Otherwise you can just use a calculator.

Provemustbewithoutcalculation.Otherwiseyoucanjustuseacalculator.

Answered by mahdipoor last updated on 02/Apr/23

(5^(100) /2^(234) )=((5×125^(33) )/(8×128^(33) ))<1⇒5^(100) <2^(234)

51002234=5×125338×12833<15100<2234

Commented by Frix last updated on 02/Apr/23

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Commented by mr W last updated on 02/Apr/23

nice!

nice!

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