Consecutive vs Odd and Even (Part 6)

Algebra Level 1

What inequality sign should we place inside the square box?

$\large{1234^{5678} \quad {\huge\square} \quad 2468^{3579}}$

There is more consecutive war here .

= > <

3 solutions

Ryan Tamburrino
Aug 15, 2015

Note that $2468=2\cdot 1234$ . Thus, we want to see if $\dfrac{1234^{5678}}{1234^{3579}} = 1234^{2099} > 2^{3579}$ . Clearly, we have $1234^{2099} > 1024^{2099} = (2^{10})^{2099} = 2^{20990} > 2^{3579}$ , hence the answer.

2^3579 *

Kobi Shiran - 5 years, 10 months ago

Oops, didn't catch that! Fixed. I'll add some more lines to the solution.

Ryan Tamburrino - 5 years, 10 months ago

Caner Uler
Nov 29, 2015

Take the logarithm of both sides and then compare the numbers. The first one is bigger than the second one.

Iqbal Mohammad
Nov 30, 2015

This hold true for:

For a > 2 and n >0:

a^n > 2^n

Multiply both sides with a^n

(a^2n) > ( a^n) x (2^n)

Hence proved (a^2n) > ( 2a)^n

Consecutive vs Odd and Even (Part 6)

There is more consecutive war here .

3 solutions

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