To solve this inequality, we need to first simplify both sides.
Starting with the left side of the inequality:
Log₂ ₓ₊₂(x-18)² + 32
Using the property of logarithms that logₐ(b) = c is equivalent to a^c = b, we can rewrite the left side as:
2^((x+2)-18)^2 + 32
Now, simplifying further:
2^(x-16)^2 + 32
Now, let's simplify the right side of the inequality:
16logₓ₊₂(36+16x-x²)
Using the same property of logarithms as before, we can rewrite this as:
x₊₂^(36+16x-x²) = 16
Now, we have the updated inequality:
2^(x-16)^2 + 32 ≤ x₊₂^(36+16x-x²) = 16
We can continue simplifying and solving from here, depending on the specific values and relationships of x in the inequality.
To solve this inequality, we need to first simplify both sides.
Starting with the left side of the inequality:
Log₂ ₓ₊₂(x-18)² + 32
Using the property of logarithms that logₐ(b) = c is equivalent to a^c = b, we can rewrite the left side as:
2^((x+2)-18)^2 + 32
Now, simplifying further:
2^(x-16)^2 + 32
Now, let's simplify the right side of the inequality:
16logₓ₊₂(36+16x-x²)
Using the same property of logarithms as before, we can rewrite this as:
x₊₂^(36+16x-x²) = 16
Now, we have the updated inequality:
2^(x-16)^2 + 32 ≤ x₊₂^(36+16x-x²) = 16
We can continue simplifying and solving from here, depending on the specific values and relationships of x in the inequality.