Solve 0.6^x < 0.8

Question

So here's what I did:
x log0.6 < log 0.8
x < log 0.8/ log 0.6
x < 0.437
But that's not the correct answer, it's:
x > 0.437
Can someone explain why it changes < from to > ? Thanks in advance!

Answer 1

let's pick it up from
x log0.6 < log 0.8 , now put in the actual values
x(-.22185) < -.09691
to get x, we would have to divide both sides by -.22185
BUT, remember if you divide an inequality by a negative
you must reverse the inequality sign

x(-.22185)/-.22185 > -.09691/-.22185
x > .4368

Consider the graph of y = .6^x
see here:
www.wolframalpha.com/input/?i=plot+y+%3D+(.6)%5Ex+,+y+%3D+.8

notice that the curve is below y = .8 for all x's > .4368

Answer 2

Ah, that never occurred to me! Thank you for the easy-to-understand explanation!