Inequality!

Algebra Level 2

Given that $\log 343=2.5353$ , find the smallest integer $n$ such that

$\large 7^n > 10^5$

1 solution

Md Zuhair
Dec 19, 2016

First of all taking log on both sides with base 10, we get,

$n log_{10}7 > 5 log_{10}10$

Hence $n > 5/ log_{10}7$

hence $n>5.91...$ or for least integer $n=6$