Evaluate log base 7 of 1

Problem

(log_7)(1)

Solution

1. Identify the logarithmic expression, which asks for the exponent x such that the base 7 raised to the power of x equals the argument 1

2. Rewrite the expression in exponential form using the definition (log_b)(a)=x⇔bx=a

7=1

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

7=1

4. Conclude that the value of the exponent x must be 0

x=0

Final Answer

(log_7)(1)=0

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