Question and Answers Forum

All Questions      Topic List

Arithmetic Questions

Previous in All Question      Next in All Question      

Previous in Arithmetic      Next in Arithmetic      

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

$$whichislarger,$$$$2^{234}or{5}^{100}?$$

Answered by aba last updated on 02/Apr/23

$$2^{234}>5^{100}$$

Commented by Frix last updated on 02/Apr/23

$$\mathrm{Prove}\mathrm{it}?$$

Answered by nikif99 last updated on 02/Apr/23

$$234\log 2\lessgtr 100\log 5=100\left(\log \left(\frac{10}{2}\right)\right)=$$$$100(\log 10-\log 2)=100-100\log 2\Rightarrow$$$$234\log 2\lessgtr 100-100\log 2\Rightarrow$$$$334\log 2\lessgtr 100\Rightarrow 334\times 0.30103>100$$

Commented by Frix last updated on 02/Apr/23

$$\mathrm{Prove}\mathrm{must}\mathrm{be}\mathrm{without}\mathrm{calculation}.$$$$\mathrm{Otherwise}\mathrm{you}\mathrm{can}\mathrm{just}\mathrm{use}\mathrm{a}\mathrm{calculator}.$$

Answered by mahdipoor last updated on 02/Apr/23

$$\frac{5^{100}}{2^{234}}=\frac{5\times {125}^{33}}{8\times {128}^{33}}<1\Rightarrow 5^{100}<2^{234}$$

Commented by Frix last updated on 02/Apr/23

��

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

$$nice!$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com