Understanding the Components of the Logarithmic Function f(x) = log₂(x+2)

f(x) = log₂(x+2)

The function f(x) = log₂(x+2) represents a logarithmic function with a base of 2

The function f(x) = log₂(x+2) represents a logarithmic function with a base of 2. Let’s understand the different components of this function.

The letter ‘x’ represents the input or independent variable of the function. It represents the values for which you want to evaluate the function. In this case, x represents the input values that will be plugged into the equation.

The expression (x+2) inside the logarithm represents the argument of the function. It is the value that will be operated on by the logarithm. In this case, the argument is (x+2), which means that you will add 2 to the value of x and then take the logarithm of that sum.

The logarithmic function function log₂(x) with base 2 evaluates the exponent to which 2 must be raised in order to obtain the value x. In other words, if 2 is raised to the power of the output of the logarithm, it will equal to the argument (x+2).

For example, if you want to find f(4), you would substitute 4 for x in the original equation:

f(x) = log₂(x+2)
f(4) = log₂(4+2)

Now, evaluate the argument:

f(4) = log₂(6)

To find the value of log₂(6), you need to determine to what power 2 must be raised to get 6. Logarithm is essentially the inverse operation of exponentiation. So, in this case, you are looking for the exponent in the equation 2^x = 6.

In this case, 2^2 = 4 and 2^3 = 8. Since 6 is between 4 and 8, you can estimate that log₂(6) is between 2 and 3. With more precise calculations, you can find that log₂(6) is approximately equal to 2.585.

Therefore, f(4) ≈ 2.585.

You can apply the same method to find the value of f(x) for any other value of x by substituting it into the equation and solving for the logarithm.

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