Question

Arranging the logarithmic functions from greatest to least:

a) f(x)=log(x−3)
b) f(x)=log(x+4)
c) f(x)=−log(x−4)
d) f(x)=−log(x+3)

Answer 1

To arrange the logarithmic functions from greatest to least, compare their bases and the arguments inside the logarithm. The larger the base, the greater the value of the logarithmic function. The smaller the argument, the greater the value of the logarithmic function.

Step-by-step explanation:

To arrange the logarithmic functions from greatest to least, we need to compare their bases. The larger the base, the greater the value of the logarithmic function.

So, comparing the given functions:

• f(x) = log(x−3) - Base: 10
• f(x) = log(x+4) - Base: 10
• f(x) = −log(x−4) - Base: 10
• f(x) = −log(x+3) - Base: 10

All the functions have the same base (10), so we need to compare the arguments inside the logarithm. The smaller the argument, the greater the value of the logarithmic function.

Comparing the arguments:

• x−3
• x+4
• x−4
• x+3

Considering the above comparisons, the arranged logarithmic functions from greatest to least are:

1. f(x) = log(x−3)
2. f(x) = −log(x+4)
3. f(x) = log(x+3)
4. f(x) = −log(x−4)