Question-137065

Question Number 137065 by mr W last updated on 29/Mar/21

Commented by mr W last updated on 29/Mar/21

w h i c h n u m b e r i s l a r g e r ?

Answered by mr W last updated on 30/Mar/21

3^{2} = 9 > 8.8 = 1.1 \times 8 = (1 + 0.1) \times 2^{3}

{(3^{2})}^{50} > {(1 + 0.1)}^{50} \times {(2^{3})}^{50}

3^{100} > {(1 + 0.1)}^{50} \times 2^{150} > (1 + 50 \times 0.1) \times 2^{150} = 6 \times 2^{150}

\frac{1}{2} \times 3^{100} > 3 \times 2^{150} > 2^{150}

2^{2} = 4 > 3

{(2^{2})}^{\frac{1}{2} \times 3^{100}} > 3^{2^{150}}

\Rightarrow 2^{3^{100}} > 3^{2^{150}}

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