Question

Inequality with variables in power:
x^(x+6) < x^(4x-3)
-------------------
same bases so:
x+6 < 4x-3
9 < 3x
3 < x

I got that answer right, but there is another answer that I don't know how to find which is "0 11 years ago

Answer 1

\[x ^{\left( x+6 \right)}<x ^{\left( x+3 \right)}\]
\[x ^{\left( x+3+3 \right)}-x ^{\left( x+3 \right)}<0,x ^{\left( x+3 \right)}\left( x^3-1 \right)<0\]

Answer 2

both the factors are of different sign.

Answer 3

if x>1,then both the factors are positive.
if x=1 then the product is 0.
so x<1

Answer 4

\[hence x^3-1<0,so~ x ^{\left( x+3 \right)}>0\]

Answer 5

Assuming the inequality was an equation, the answers would be x=3 and x=1, how would you find that x=1? Because 1 to any power is 1?

Answer 6

if x>0,x<1.then \[x^3<1,x^3-1<0\]