Let f(x) = log(x). find values of a such that f(3a) = 3f(a).

a = 1.7318

Step-by-step explanation:

Given function in the question f(x) = log(x)

also,

f(3a) = 3f(a)

To find: the value of 'a'

now,

f(3a) = 3f(a)

⇒ log(3a) = 3 × log(a)

now,

we know the property of the log function that

log(AB) = log(A) + log(B)

therefore,

⇒ log(3) + log(a) = 3 × log(a)

or

⇒ log(3) = 3 × log(a) -  log(a)

or

⇒ 2log(a) = log(3)

now,

log(3) = 0.4771

thus,

⇒ 2log(a) = 0.4771

or

log(a) = 0.2385

taking anti-log both sides, we get

a =

or

a = 1.7318

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5