Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Which expression is equivalent to [tex]\log _2 9 x^3[/tex]?

A. [tex]\log _2 9+3 \log _2 x[/tex]

B. [tex]\log _2 x+3 \log _2 9[/tex]

C. [tex]3 \log _2 x-\log _2 9[/tex]

D. [tex]3 \log _2 9-\log _2 x[/tex]

Sagot :

GinnyAnswer
To determine which expression is equivalent to \(\log_2 (9x^3)\), we can use the properties of logarithms.

1. Product Rule of Logarithms: \(\log_b (MN) = \log_b M + \log_b N\)

Applying the product rule to \(\log_2 (9x^3)\):
[tex]\[ \log_2 (9x^3) = \log_2 9 + \log_2 x^3 \][/tex]

2. Power Rule of Logarithms: \(\log_b (M^k) = k \log_b M\)

Applying the power rule to \(\log_2 x^3\):
[tex]\[ \log_2 x^3 = 3 \log_2 x \][/tex]

Now, substitute back into the equation from the product rule:
[tex]\[ \log_2 (9x^3) = \log_2 9 + 3 \log_2 x \][/tex]

Therefore, the expression equivalent to \(\log_2 (9x^3)\) is:
[tex]\[ \log_2 9 + 3 \log_2 x \][/tex]

Hence, the correct answer is:
[tex]\[ \log_2 9 + 3 \log_2 x \][/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.