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

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it