It's almost 1,right?

Algebra Level 2

Which is bigger ( 21 20 ) 100 or 100 ? \color{#3D99F6}{\left(\dfrac{21}{20}\right)^{100}} \quad \text{or} \quad \color{#D61F06}{100}~?

( 21 20 ) 100 \left(\dfrac{21}{20}\right)^{100} 100 100

Rohit Udaiwal by Rohit Udaiwal , 20, India

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1 solution

Applying log ⁡ 100 \log_{100} to both the terms, we get 100 log ⁡ 100 21 20 > 1 ( Since 21/20 is greater than 1 ) 100\log_{100}{\frac{21}{20}}>1(\color{#D61F06}{\text{Since 21/20 is greater than 1}}) and 1 1 respectively.

Therefore, ( 21 20 ) 100 > 100 (\frac{21}{20})^{100}>100 .

6 Helpful 0 Interesting 0 Brilliant 0 Confused

How do we know that log ⁡ 100 21 20 > 1 100 \log_{100} \frac{21}{20} > \frac{1}{100} ?

Chaitanya Rao - 1 year, 7 months ago

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