The value of X , if log1/2?x >= log1/3?x is

Question

The value of X , if log_1/2x >= log_1/3x is 

Answer 1

logx to the base 1/2 = logx/log1/2 = about - logx/.3

logx to the base 1/3 = logx/log1/3 = about -logx/.48

-logx/.3 > -logx/.48

multiply by -1 will reverse the direction of the inequality sign

logx/.3 < logx/.48

.48logx < .3logx

x < 1

when x=1, both sides are equal since logx =0