Is 100^500 bigger or 1000^300?
\(100^{500} \\ or\\ 1000^{300} =(100^{10})^{300} = 100^{3000}\)
Can you tell me which is bigger now?
1000^300=[(100)^1.5]^300=100^450, Therefore
100^500>100^450.
Another way of comparing is to take their logs as follows:
Log:100^500=1,000
Log: 1000^300=900, therefore
1,000>900
100^500 = (10^2)^500 = 10^1000
1000^300 = (10^3)^300 = 10^900
Which is bigger? 100^500
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