Question

expand log_1/2(3x^2/2) using the properties and rules for logarithms
A. log_1/2(3)+2log(x)- log_1/2(2)
B. log_1/2(3)+2log_1/2(x)+1
C. 2log_1/2(3x)+1
D. 2log_1/2(3x)- log_1/2(2)

Answer 1

B.

Answer 2

its B. log_1/2(3)+2log_1/2(x)+1

Answer 3

Using the properties and rules for logarithms, we can rewrite the expression as:

log_1/2(3x^2/2) = log_1/2(3) + log_1/2(x^2/2) [using the rule log(x*y) = log(x) + log(y)]

Next, we can use the rule log(a^b) = b*log(a) to simplify the expression further:

= log_1/2(3) + log_1/2(x^(2/2)) - log_1/2(2) [since 2/2 = 1]

= log_1/2(3) + log_1/2(x) - log_1/2(2)

Therefore, the expanded form of log_1/2(3x^2/2) using the properties and rules for logarithms is A. log_1/2(3) + 2log_1/2(x) - log_1/2(2).

Answer 4

Apologies for the mistake. Let's recheck the steps:

Using the properties and rules for logarithms, we can expand the expression log_1/2(3x^2/2) as follows:

log_1/2(3x^2/2)

= log_1/2(3) + log_1/2(x^2/2) [Using property 1]

= log_1/2(3) + log_1/2(x^2) - log_1/2(2) [Using property 2]

Now, we simplify the log_1/2(x^2). We use property 2 again:

= log_1/2(3) + 2 * log_1/2(x) - log_1/2(2) [Using property 2]

Therefore, the correct expanded form of log_1/2(3x^2/2) using the properties and rules for logarithms is not option B, but option A:

A. log_1/2(3) + 2*log(x) - log_1/2(2)

Answer 5

Apologies for the confusion. Let's go through the steps again to confirm:

Using the properties and rules for logarithms, we can expand the expression log_1/2(3x^2/2) as follows:

log_1/2(3x^2/2)

= log_1/2(3) + log_1/2(x^2/2) [Using property 1]

= log_1/2(3) + log_1/2(x^2) - log_1/2(2) [Using property 2]

Now, we simplify the log_1/2(x^2). We can use property 2 again:

= log_1/2(3) + 2 * log_1/2(x) - log_1/2(2) [Using property 2]

The expanded form of log_1/2(3x^2/2) using the properties and rules for logarithms is indeed option B:

B. log_1/2(3) + 2*log_1/2(x) + 1

Once again, apologies for the confusion earlier. The correct answer is option B.