log9 1
Understand the Problem
The question is asking for the logarithm of 1 with a base of 9. The logarithm of any number 1 is always 0, regardless of the base. This is based on the definition of logarithms.
Answer
$\log_{9}(1) = 0$
Answer for screen readers
The final answer is $\log_{9}(1) = 0$.
Steps to Solve
- Understanding the definition of logarithm
The logarithm function asks the question: to what power must the base be raised to produce a given number? In this case, we want to find the power to which 9 must be raised to equal 1.
- Applying the definition to the problem
We set up the equation based on the definition of logarithms: $$ \log_{9}(1) = x $$ This translates to finding $x$ such that: $$ 9^x = 1 $$
- Solving the equation
Since any number raised to the power of 0 equals 1, we can conclude: $$ 9^0 = 1 $$
This means that: $$ x = 0 $$
- Concluding the result
Therefore, we find: $$ \log_{9}(1) = 0 $$
The final answer is $\log_{9}(1) = 0$.
More Information
The property that the logarithm of 1 is always 0 holds true for any positive base greater than 0. This is a fundamental property of logarithms, showing that no matter what the base is, raising a base to the power of 0 will always give 1.
Tips
A common mistake is forgetting that the logarithm of 1 is always 0, regardless of the base. To avoid this, remember the fundamental rule that for any base $b$, $b^0 = 1$.
