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)
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).
To expand the logarithmic expression log_1/2(3x^2/2), we can use the following properties and rules for logarithms:
1. log_a(bc) = log_a(b) + log_a(c)
2. log_a(b^c) = c * log_a(b)
3. log_a(a) = 1
Applying these rules, let's expand the expression step-by-step:
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 need to 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]
Therefore, the expanded form of log_1/2(3x^2/2) using the properties and rules for logarithms is option A:
A. log_1/2(3) + 2*log(x) - log_1/2(2)
B.
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)
its B. log_1/2(3)+2log_1/2(x)+1
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.
To expand log_1/2(3x^2/2) using the properties and rules for logarithms, we can use the following rules:
1. log_a(bc) = log_a(b) + log_a(c)
2. log_a(b^c) = c*log_a(b)
Let's break down the given expression step by step:
log_1/2(3x^2/2)
Using rule 1, we can separate the numerator and denominator of the fraction:
= log_1/2(3) + log_1/2(x^2/2)
Now, let's focus on the numerator first:
= log_1/2(3) + log_1/2(x^2) - log_1/2(2)
We can simplify the second term using rule 2:
log_1/2(x^2) = 2*log_1/2(x)
Now, our expression becomes:
= log_1/2(3) + 2*log_1/2(x) - log_1/2(2)
Therefore, the correct answer is A. log_1/2(3) + 2*log_1/2(x) - log_1/2(2).