To solve this inequality, we will first simplify the expression:
log1/6(log2√(6-x)) > log(2√(6-x)) > log2 + log√(6-x) > log2 + 1/2log(6-x) > log2 + log(6-x) > log(2(6-x)) > log(12-2x) > 0
Now, we will rewrite the inequality in exponential form:
12 - 2x > -2x > -1x < 11/2
Therefore, the solution to the inequality is x < 5.5.
To solve this inequality, we will first simplify the expression:
log1/6(log2√(6-x)) >
log(2√(6-x)) >
log2 + log√(6-x) >
log2 + 1/2log(6-x) >
log2 + log(6-x) >
log(2(6-x)) >
log(12-2x) > 0
Now, we will rewrite the inequality in exponential form:
12 - 2x >
-2x > -1
x < 11/2
Therefore, the solution to the inequality is x < 5.5.