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Determine, without a calculator, which is greater 4^100 or 6^75 (show full working)

 

Thankyou!

 
mattkuk2003  Nov 8, 2018
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Determine, without a calculator, which is greater 4^100 or 6^75

 

\(\begin{array}{|rcl|cl|} \hline && 4^{100} && 6^{75} \\ &=& 4^{4\cdot 25} &=& 6^{3\cdot 25} \\ &=& \left(4^4\right)^{25} &=& \left(6^3\right)^{25} \\ &=& 256^{25} &=& 216^{25} \\ \hline \end{array} \)

 

\(\text{So $4^{100}$ is greater than $6^{75}$ }\)

 

laugh

 
heureka  Nov 8, 2018

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