1Cademy - Try It 10.55: Evaluating $$\log_{13} 1$$ and $$\log

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Logarithm of 1 Property

Example

Try It 10.55: Evaluating $\log_{13} 1$ and $\log_9 9$

Evaluate each logarithmic expression using the basic properties of logarithms.

ⓐ To evaluate $\log_{13} 1$ , apply the property $\log_a 1 = 0$ , which holds for any valid base. Since the base $13$ satisfies $a > 0$ and $a eq 1$ , the expression evaluates to $0$ . Therefore, $\log_{13} 1 = 0$ .

ⓑ To evaluate $\log_9 9$ , apply the property $\log_a a = 1$ . Since the base and the argument are both $9$ , the expression evaluates to $1$ . Therefore, $\log_9 9 = 1$ .