IDNLearn.com offers a comprehensive platform for finding and sharing knowledge. Discover detailed answers to your questions with our extensive database of expert knowledge.
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 using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.