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Answer :
To convert an exponential equation to its logarithmic form, we need to understand the relationship between them. 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]\( 13^2 = 169 \)[/tex], we want to express this in logarithmic form. Here's how we do it step-by-step:
1. Identify the base of the exponent, which is [tex]\( 13 \)[/tex].
2. Identify the result or the number on the right side of the equation, which is [tex]\( 169 \)[/tex].
3. Identify the exponent, which is [tex]\( 2 \)[/tex].
Now, use these to write the logarithmic form:
- Base (a): 13
- Result (c): 169
- Exponent (b): 2
In logarithmic form, you state that the logarithm of the result, 169, with base 13 is equal to the exponent, 2. So the equation becomes:
[tex]\[
\log_{13} 169 = 2
\][/tex]
Therefore, the correct logarithmic form of the given equation [tex]\( 13^2 = 169 \)[/tex] is [tex]\( \log_{13} 169 = 2 \)[/tex].
Given the exponential equation [tex]\( 13^2 = 169 \)[/tex], we want to express this in logarithmic form. Here's how we do it step-by-step:
1. Identify the base of the exponent, which is [tex]\( 13 \)[/tex].
2. Identify the result or the number on the right side of the equation, which is [tex]\( 169 \)[/tex].
3. Identify the exponent, which is [tex]\( 2 \)[/tex].
Now, use these to write the logarithmic form:
- Base (a): 13
- Result (c): 169
- Exponent (b): 2
In logarithmic form, you state that the logarithm of the result, 169, with base 13 is equal to the exponent, 2. So the equation becomes:
[tex]\[
\log_{13} 169 = 2
\][/tex]
Therefore, the correct logarithmic form of the given equation [tex]\( 13^2 = 169 \)[/tex] is [tex]\( \log_{13} 169 = 2 \)[/tex].
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