Answer :
To determine which logarithmic equation is equivalent to the given exponential equation [tex]\(2^x = 32\)[/tex], let's review the relationship between exponential and logarithmic forms.
An exponential equation of the form [tex]\(a^b = c\)[/tex] can be rewritten in logarithmic form as [tex]\(\log_a(c) = b\)[/tex].
Given the exponential equation:
[tex]\[ 2^x = 32 \][/tex]
We need to express this in logarithmic form. According to the logarithmic definition:
1. The base [tex]\(a\)[/tex] of the exponential (which is 2 in this case) becomes the base of the logarithm.
2. The exponent [tex]\(b\)[/tex] (which is [tex]\(x\)[/tex] in this case) becomes the result of the logarithm.
3. The result [tex]\(c\)[/tex] (which is 32 in this case) becomes the argument of the logarithm.
So, applying these rules, we convert [tex]\(2^x = 32\)[/tex] into logarithmic form as:
[tex]\[ \log_2(32) = x \][/tex]
Therefore, the correct logarithmic equation is:
[tex]\[ \log_2 32 = x \][/tex]
Thus, the answer is:
[tex]\[ \log_2 32 = x \][/tex]
An exponential equation of the form [tex]\(a^b = c\)[/tex] can be rewritten in logarithmic form as [tex]\(\log_a(c) = b\)[/tex].
Given the exponential equation:
[tex]\[ 2^x = 32 \][/tex]
We need to express this in logarithmic form. According to the logarithmic definition:
1. The base [tex]\(a\)[/tex] of the exponential (which is 2 in this case) becomes the base of the logarithm.
2. The exponent [tex]\(b\)[/tex] (which is [tex]\(x\)[/tex] in this case) becomes the result of the logarithm.
3. The result [tex]\(c\)[/tex] (which is 32 in this case) becomes the argument of the logarithm.
So, applying these rules, we convert [tex]\(2^x = 32\)[/tex] into logarithmic form as:
[tex]\[ \log_2(32) = x \][/tex]
Therefore, the correct logarithmic equation is:
[tex]\[ \log_2 32 = x \][/tex]
Thus, the answer is:
[tex]\[ \log_2 32 = x \][/tex]
