Question
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Write the expression below as a single logarithm in simplest form.
\[
\log _{b} 6-\log _{b} 6
\]
Answer Attempt 1 out of 2
\[
\log _{b}
\]
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Answer
So, the simplified form of the expression \( \log _{b} 6-\log _{b} 6 \) is \( \boxed{0} \).
Step 1 ：The question is asking to simplify the expression \( \log _{b} 6-\log _{b} 6 \).
Step 2 ：From the properties of logarithms, we know that the difference of two logarithms with the same base is equivalent to the logarithm of the quotient of the numbers.
Step 3 ：Therefore, we can simplify the expression as \( \log _{b} \frac{6}{6} \).
Step 4 ：Since any number divided by itself is 1, the expression simplifies to \( \log _{b} 1 \).
Step 5 ：Finally, the logarithm of any base to the power of 1 is always 0.
Step 6 ：So, the simplified form of the expression \( \log _{b} 6-\log _{b} 6 \) is \( \boxed{0} \).
