Question

Check whether the logarithm log, (5-2x) is defined for each of the following: (a)x=2 (b) x=0.5 (c) x=3 (d) x=2.5 (e) x = 1 (0)x= 2

Answer 1

See explanation below

Explanation:

The function

f(w) = log(w) is only defined when w > 0,

so, in order that the function

f(x) = log(5-2x) is defined, we must have

5-2x > 0
`\bf \rightarrow` 2x < 5
`\bf \rightarrow x<(5)/(2)=2.5`

a) x = 2

2 < 2.5, so f is defined in x=2

b) x=0.5

0.5 < 2.5, so f is defined in x=0.5

c) x = 3

3 > 2.5, so f is not defined in x=3

d) x=2.5

2.5 is not less than 2.5, so f is not defined in x=2.5

e) x=1

1 < 2.5, so f is defined in x=1

f) x=2

2 < 2.5, so f is defined in x=2