Questions: Use the properties of logarithms to evaluate the expression without the use of a calculator. [ log a a, a>1 log a a= ]

Transcript text: Use the properties of logarithms to evaluate the expression without the use of a calculator. \[ \begin{array}{r} \log _{a} a, a>1 \\ \log _{a} a=\square \end{array} \] $\square$

Solution

Solution Steps

To evaluate the expression $\log_{a} a$, we can use the property of logarithms that states $\log_{b} b = 1$ for any base $b > 0$. This is because the logarithm of a number to its own base is always 1.

Step 1: Understanding the Logarithmic Property

We start with the expression $\log_{a} a$. According to the properties of logarithms, specifically the identity $\log_{b} b = 1$ for any base $b > 0$, we can directly evaluate this expression.

Step 2: Applying the Property

Since $a > 1$, we can apply the property: \[ \log_{a} a = 1 \]