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Can someone help me please.

Can someone help me please.-example-1
User Rbhalla
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Explanation:

2^x < 2x³ + 1 ?

that would mean

x < log2(2x³ + 1)

x < log2(2×(x³ + 1/2))

x < log2(2) + log2(x³ + 1/2)

x < 1 + log2(x³ + 1/2)

x - 1 < log2(x³ + 1/2)

for large x the "-1" and the "+ 1/2" are becoming relatively irrelevant for the inequality.

and the limes of this goes to

x < log2(x³)

which is not true for large x, as the logarithm turns into a very flat curve, while "x" just keeps growing with slope 1 and therefore outpaces the logarithm.

for x = 20 for example, 2^x is already way larger than 2x³.

the "cross-over" point is between x=11 and x=12.

from there on 2^x will quickly become much larger than 2x³ + 1.

User Rajeev Sreedharan
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8.5k points

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