SOLUTION: {{{(1/81)^(4m+1)>(1/27)^5*m}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: {{{(1/81)^(4m+1)>(1/27)^5*m}}}       Log On


   

Question 939942: %281%2F81%29%5E%284m%2B1%29%3E%281%2F27%29%5E5%2Am
Found 2 solutions by brysca, laoman:
Answer by brysca(112) About Me  (Show Source):
You can put this solution on YOUR website!
solution posted below
.
hope this helps!

Answer by laoman(51) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F81%29%5E%284m%2B1%29%3E%281%2F27%29%5E5%2Am
Ok, let's simplify this using indices
1%2F81+=+1%2F3%5E4+=+3%5E-4 and 1%2F27=+1%2F3%5E3+=+3%5E-3
Knowing the above, we can simplify the inequality to become
3%5E%28-4%2A%284m%2B1%29%29+%3E+3%5E%283%2A5%2Am%29
Since the bases on both sides are equal, let's take the inequalities of the powers alone
-4*(4m+1)>-3*5m
-16m-4>-15m
Let's add 16m to both sides
-16m+4+16m>-15m+16m
4>m
m<4 since it has been reversed