Questions: What happens to the value of f(x)=log4 x as x approaches 0 from the right? f(x) approaches negative infinity

Transcript text: What happens to the value of $f(x)=\log _{4} x$ as $x$ approaches 0 from the right? $f(x)$ approaches negative infinity

Solution

Solution Steps

Step 1: Analyze the behavior of $ f(x) = \log_{4} x $ as $ x $ approaches 0 from the right

The logarithmic function $ \log_{4} x $ is defined for $ x > 0 $.
As $ x $ approaches 0 from the right ($ x \to 0^+ $), $ \log_{4} x $ tends to negative infinity because the logarithm of a very small positive number is a large negative number.

Step 2: Analyze the behavior of $ f(x) = \log_{4} x $ as $ x $ approaches infinity

As $ x $ approaches infinity ($ x \to +\infty $), $ \log_{4} x $ tends to positive infinity because the logarithm of a very large number is a large positive number.

Step 3: Interpret the given options for the behavior of $ f(x) $ as $ x $ approaches infinity

The options provided are:
1. $ f(x) $ approaches negative infinity
2. $ f(x) $ approaches 0
3. $ f(x) $ approaches infinity
From Step 2, we know that $ f(x) $ approaches infinity as $ x \to +\infty $, so the correct option is $ f(x) $ approaches infinity.

Final Answer

As $ x $ approaches 0 from the right, $ f(x) $ approaches $ -\infty $.
As $ x $ approaches $ +\infty $, $ f(x) $ approaches $ +\infty $.
Thus, the final answers are:

$ \boxed{-\infty} $
$ \boxed{+\infty} $

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

Next >

Thank you for your feedback.

Copied!