Create equivalent expressions in the equation that all have equal bases, then solve for x.
x<0
Let's solve your inequality step-by-step:
6^x<3^x
Let's find the critical points of the inequality.
6^x=3^x
Solve Exponent.
6^x=3^x
log(6^x)=log(3^x) (Take log of both sides)
x*(log(6))=x*(log(3))
x=(log(3)/log(6))*(x)
x=0.613147*x
x=0.613147x (Simplify both sides of the equation)
x−0.613147x=0.613147x−0.613147x (Subtract 0.613147x from both sides)
0.386853x=0
0.386853x/0.386853=0/0.386853 (Divide both sides by 0.386853)
x=0
Critical points:
x=0
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x<0 (Works in original inequality)
x>0 (Doesn't work in original inequality)
Answer:
x<0
