Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Let's start by understanding the relationship between exponential equations and logarithmic equations.
The general rule for converting an exponential equation to a logarithmic equation is as follows:
- If you have an exponential equation of the form [tex]\(a^b = c\)[/tex], you can convert it into the logarithmic form as [tex]\(\log_a(c) = b\)[/tex].
Given the exponential equation [tex]\(6^x = 216\)[/tex]:
1. Identify the base [tex]\(a\)[/tex], exponent [tex]\(b\)[/tex], and the result [tex]\(c\)[/tex]. Here, [tex]\(a = 6\)[/tex], [tex]\(b = x\)[/tex], and [tex]\(c = 216\)[/tex].
2. Apply the rule for converting exponential equations to logarithmic equations. According to the rule, we can write:
[tex]\[ \log_6 (216) = x \][/tex]
This logarithmic equation [tex]\(\log_6 (216) = x\)[/tex] represents the relationship in terms of logarithms.
Therefore, the correct logarithmic equation equivalent to the given exponential equation [tex]\(6^x = 216\)[/tex] is:
[tex]\[ \log_6 (216) = x \][/tex]
This corresponds to option C. So, the correct answer is:
C. [tex]\(\log_6 (216) = x\)[/tex]
The general rule for converting an exponential equation to a logarithmic equation is as follows:
- If you have an exponential equation of the form [tex]\(a^b = c\)[/tex], you can convert it into the logarithmic form as [tex]\(\log_a(c) = b\)[/tex].
Given the exponential equation [tex]\(6^x = 216\)[/tex]:
1. Identify the base [tex]\(a\)[/tex], exponent [tex]\(b\)[/tex], and the result [tex]\(c\)[/tex]. Here, [tex]\(a = 6\)[/tex], [tex]\(b = x\)[/tex], and [tex]\(c = 216\)[/tex].
2. Apply the rule for converting exponential equations to logarithmic equations. According to the rule, we can write:
[tex]\[ \log_6 (216) = x \][/tex]
This logarithmic equation [tex]\(\log_6 (216) = x\)[/tex] represents the relationship in terms of logarithms.
Therefore, the correct logarithmic equation equivalent to the given exponential equation [tex]\(6^x = 216\)[/tex] is:
[tex]\[ \log_6 (216) = x \][/tex]
This corresponds to option C. So, the correct answer is:
C. [tex]\(\log_6 (216) = x\)[/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.