Question

Log 1/3 (log2 (12 – x)) > –2

Answer 1

{12-X>0⇒X<12
{log(2)(12-x)>0⇒12-x>1⇒x<11
{log(2)(12-x)<9⇒12-x<512⇒x>-500
x∈(-500;11)

Answer 2

We can solve this inequality by using the following steps:

Step 1: Solve the inner logarithmic expression.

log2 (12 – x) > 3

Step 2: Convert the base of the logarithm to a common base.

log2 (12 – x) = log(12 – x)/log2

Step 3: Substitute the expression from step 2 into the original inequality.

log1/3 (log(12 – x)/log2) > –2

Step 4: Simplify the inequality by multiplying both sides by log2 and dividing by –log1/3.

log(12 – x) < –2(log2)(log1/3)

Step 5: Solve for x.

log(12 – x) < –2(log2)(log1/3)

12 – x < 2–2(log2)(log1/3)

x > 12 – 2–2(log2)(log1/3)

Therefore, the solution to the inequality is x > 12 – 2–2(log2)(log1/3).