Exploring the Behavior of the Logarithmic Function f(x) = log₂x+2 | Step-by-Step Analysis & Examples

f(x) = log₂x+2

To understand the function f(x) = log₂x+2, let’s break it down step by step

To understand the function f(x) = log₂x+2, let’s break it down step by step.

1. The function is defined as f(x) which means we are expressing the function in terms of the variable x.

2. The expression log₂x represents the logarithm of x to the base 2.

– Logarithm: A logarithm is an operation that tells us how many times one number (the base) must be multiplied by itself to give another number. In this case, we are using a base of 2, so the logarithm of x to the base 2, log₂x, is the exponent to which 2 needs to be raised to get x. For example, log₂4 = 2 because 2 raised to the power of 2 is equal to 4.

3. The expression +2 is added to the logarithm. This means that after finding the logarithm of x to the base 2, we add 2 to the result.

Let’s now understand how the function f(x) behaves by evaluating it for certain values of x.

1. For x = 1:
f(1) = log₂1 + 2
= 0 + 2
= 2

2. For x = 2:
f(2) = log₂2 + 2
= 1 + 2
= 3

3. For x = 4:
f(4) = log₂4 + 2
= 2 + 2
= 4

From these examples, we can observe that as x increases, the value of f(x) also increases. This is because the logarithm of a larger number is itself a larger number, and when we add 2 to it, the result gets bigger.

In general, the function f(x) = log₂x+2 represents a logarithmic function with a base of 2, where the output value varies depending on the input value x.

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