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

cut 138 centimeters off

step-by-step explanation:

250-112 = 138

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240