# Math Help - 2^x≤ 3^x

1. ## 2^x≤ 3^x

Express as an integer the smallest real number x such that
$2^x$ $3^x$

2. Originally Posted by yoman360
Express as an integer the smallest real number x such that
$2^x$ $3^x$
by inspection, x = 0 is the smallest integer for which this works.

you can compute this by trying to solve the inequality (take the log of both sides to solve it, then take the smallest integer value in your solution set)

3. Originally Posted by yoman360
Express as an integer the smallest real number x such that
$2^x$ $3^x$
if it has to be an integer then 0.

can't be negative because the $\frac{1}{a^n}>\frac{1}{b^n}$ when n>0 and a<b.

4. HELLO : This anathor resolution
Thanks