Find the value of yy in each equation. explain how you determined the value of y.
a. y = 3^log3(3)
b. y = 3^log3(9)
c. y = 3^log3(81)
d. y = 3^log3(x)

a) 3

b) 9

c) 81

d) x

Step-by-step explanation:

We know the properties of log function as:

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

2)

3) log(aᵇ) = b × log(a)

also,

4)

Given:

a. y =

Now,

taking log both sides, we get

log(y) =

using 3, we get

log(y) = log₃(3) × log(3)

using 4, we get

log(y) =   × log(3)

or

log(y) =  1 × log(3)

taking anti-log both sides

y = 3

b. y =

Now,

taking log both sides, we get

log(y) =

using 3, we get

log(y) = log₃(9) × log(3)

using 4, we get

log(y) =   × log(3)

or

log(y) = log(9)

taking anti-log both sides

y = 9

c. y =

Now,

taking log both sides, we get

log(y) =

using 3, we get

log(y) = log₃(81) × log(3)

using 4, we get

log(y) =   × log(3)

or

log(y) =  log(81)

taking anti-log both sides

y = 81

d. y =

Now,

taking log both sides, we get

log(y) =

using 3, we get

log(y) = log₃(x) × log(3)

using 4, we get

log(y) =   × log(3)

or

log(y) =  log(x)

taking anti-log both sides

y = x

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!