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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 \( \boxed{0} \).

Steps

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 \( \boxed{0} \).

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