# Solve for x

1. Nov 25, 2014

### Ashes Panigrahi

1. The problem statement, all variables and given/known data
$81^5>32^x$
Find the maximum value of $x$ in order to satisfy the inequality.

2. Relevant equations
Inequalities, indices

3. The attempt at a solution
Try to make the bases on both sides of the inequality same.

2. Nov 25, 2014

### ShayanJ

You can't make the bases equal because $81=3^4$ and $32=2^5$. You should solve $81^5=32^x$ for x. That'll be the maximum value! Just get the logarithm(in any base) of both sides. That'll get out x in a way that you can isolate it.

3. Nov 25, 2014

### Staff: Mentor

Actually, you can make the bases equal.
815 = (34)5 = 320, and $32 = 3^{log_3(32)}$
To the OP:
In future posts, you need to make more of an effort than this.

4. Nov 25, 2014

### Joffan

You can reduce it somewhat:

$81^5 > 32^x = 2^{5x}$
∴ ...