Question

evaluate the expression without using a calculator.
\log_{2}(\log_{5}5)
\log_{2}(\log_{5}5)=\square

Explanation:

Step1: Evaluate the inner logarithm

Recall the property of logarithms: $\log_{a}a = 1$ for any positive real number $a
eq1$. Here, for $\log_{5}5$, since the base and the argument are the same (both 5), by this property, $\log_{5}5 = 1$.

Step2: Evaluate the outer logarithm

Now we substitute the result of the inner logarithm into the outer one. So we need to find $\log_{2}(1)$. Recall another property of logarithms: $\log_{a}1 = 0$ for any positive real number $a
eq1$. Here, the base $a = 2$, so $\log_{2}1 = 0$.

Answer:

0