Human calculator vs. indices

Algebra Level 2

Which of the following options is the greatest?

2 300 2^{300} 3 200 3^{200} 2 100 + 3 100 2^{100}+3^{100} 4 100 4^{100} 3 50 + 4 50 3^{50}+4^{50}

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1 solution

N [ log 10 ( { 3 50 + 4 50 , 2 300 , 3 200 , 2 100 + 3 100 , 4 100 } ) ] { 30.10 , 90.31 , 95.42 , 47.71 , 60.21 } N\left[\log _{10}\left(\left\{3^{50}+4^{50},2^{300},3^{200},2^{100}+3^{100},4^{100}\right\}\right)\right] \Rightarrow \{30.10,90.31,95.42,47.71,60.21\}

The calculator solution.

I computed the numbers. Because they are huge and since we concerned only about relative magnitudes, I computed the numeric logarithms base 10. The N function converts to numbers instead of symbolic representation. Then, it was just a matter of matching the two lists.

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