To analyze the given logarithmic functions represented in the equations, let’s break them down one by one:
1. Logarithmic Function: fx = log₅(x)
This function indicates the logarithm of x with base 5. In simpler terms, it’s the power to which 5 must be raised to obtain the value of x. For example, if x = 25, then:
log₅(25) = 2
This is because 5² = 25.
2. Logarithmic Function: fx = 6log₅(x)
This function can be viewed as a scaled version of the first one. It multiplies the output of log₅(x) by 6. Thus, if we take the previous example where x = 25:
fx = 6 * log₅(25) = 6 * 2 = 12
This function essentially amplifies the value of the logarithm, suggesting a growth that is six times faster than the base function at every x.
3. Logarithmic Function: fx = log₆(x)
This represents the logarithm of x with base 6. Using the same earlier example of x = 36:
log₆(36) = 2
Because 6² = 36. This function tells us how many times we need to multiply the base 6 together to reach the value of x.
4. Logarithmic Function: fx = log₆(x)
This is the same function as the previous one, which represents the same logarithmic relationship but may have been duplicated in the context of the table you provided. As noted, when x = 36:
fx = log₆(36) = 2
Thus, all four functions illustrate distinct logarithmic relationships that can be utilized in various mathematical contexts. Always remember that the base of the logarithm indicates how quickly or slowly the function will grow in relation to its inputs.