An Interesting Sequence

Algebra Level 2

$\Large \text{Find the sequence of }\left(2^\color{#D61F06}{55}\right), \left(3^\color{#3D99F6}{44}\right), \left(4^\color{#CEBB00}{33}\right)$

4^{33}>2^{55}>3^{44}

2^{55}>4^{33}>3^{44}

4^{33}>3^{44}>2^{55}

3^{44}>2^{55}>4^{33}

They are equal.

2^{55}>3^{44}>4^{33}

3^{44}>4^{33}>2^{55}

1 solution

Edward Christian
Aug 25, 2019

$\LARGE \left(2^\color{#D61F06}{55}\right) =\left[\LARGE \left(2^\color{#D61F06}5\right)^\color{#D61F06}{11}\right]= \left(\LARGE \color{#EC7300}{32}^\color{#D61F06}{11}\right)$ $\LARGE \left(3^\color{#3D99F6}{44}\right) =\left[\LARGE \left(3^\color{#3D99F6}4\right)^\color{#3D99F6}{11}\right]= \left(\LARGE \color{#EC7300}{81}^\color{#3D99F6}{11}\right)$ $\LARGE \left(4^\color{#CEBB00}{33}\right) =\left[\LARGE \left(4^\color{#CEBB00}^3\right)^\color{#CEBB00}{11}\right]= \left(\LARGE \color{#EC7300}{64}^\color{#CEBB00}{11}\right)$ $\therefore \LARGE \left(3^\color{#3D99F6}{44}\right)>\LARGE \left(4^\color{#CEBB00}{33}\right)>\LARGE \left(2^\color{#D61F06}{55}\right)$

good problem and solution!

Brian Blass - 1 year, 5 months ago

very easy solution

Razing Thunder - 9 months, 1 week ago

An Interesting Sequence

1 solution

0 pending reports