After simplification, the expression log2 3 − 3 log2 𝑥 + 1/2 log2 (𝑥 + 1) can be reduced to?

Question

After simplification, the expression log2 3 − 3 log2 𝑥 + 1/2 log2 (𝑥 + 1) can be reduced to?

Answer 1

Using logarithm properties, we can simplify the given expression as follows:

log2 3 − 3 log2 𝑥 + 1/2 log2 (𝑥 + 1)

= log2 3 − log2 𝑥^3 + log2 (𝑥 + 1)^(1/2)

= log2 (3/(𝑥^3)) + log2 (√(𝑥 + 1))

= log2 [(3/(𝑥^3)) * √(𝑥 + 1)]

Therefore, after simplification, the expression log2 3 − 3 log2 𝑥 + 1/2 log2 (𝑥 + 1) can be reduced to log2 [(3/(𝑥^3)) * √(𝑥 + 1)].

Answer 2

I thought it was simpler at the beginning :)

Answer 3

Apologies for any confusion. Let's try to simplify the expression further.

Starting with the expression log2 3 − 3 log2 𝑥 + 1/2 log2 (𝑥 + 1), we can apply logarithm properties to simplify it.

First, we can use the power rule of logarithms which states that log(base a) b^c = c * log(base a) b.

Therefore, we can rewrite the expression as:

log2 3 − log2 (𝑥^3) + (1/2) * log2 (𝑥 + 1)

Now, we can apply another logarithm property which states that log(base a) b - log(base a) c = log(base a) (b/c).

Using this property, we can combine the first two terms as:

log2 (3/(𝑥^3)) + (1/2) * log2 (𝑥 + 1)

Finally, there isn't any further simplification possible without additional information or algebraic manipulation. Therefore, after simplification, the expression remains as log2 (3/(𝑥^3)) + (1/2) * log2 (𝑥 + 1).