Evaluate log base 6 of 6

Problem

(log_6)(6)

Solution

1. Identify the definition of a logarithm, which states that (log_b)(a)=x is equivalent to bx=a

2. Set up the equation by setting the expression equal to x

(log_6)(6)=x

3. Rewrite the logarithmic equation in exponential form.

6=6

4. Determine the exponent by recognizing that any number a is equal to a1

6=6

5. Solve for x by equating the exponents since the bases are the same.

x=1

Final Answer

(log_6)(6)=1

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