Evaluate log base 3 of 1

Problem

(log_3)(1)

Solution

1. Identify the logarithmic expression, which asks for the exponent x such that the base 3 raised to the power of x equals 1

2. Apply the definition of a logarithm by rewriting the expression in exponential form.

(log_b)(a)=x⇔bx=a

3. Substitute the given values into the exponential equation.

3=1

4. Recall the zero exponent rule, which states that any non-zero base raised to the power of 0 is equal to 1

3=1

5. Determine the value of x by comparing the exponents.

x=0

Final Answer

(log_3)(1)=0

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