Solve the following equations.
3 ⋅ 2^5x = 216

Solution: x = log(72) / (5 log(2)) = 1.233985

Step-by-step explanation:

Hi there!

We have the following equation:

3 ⋅ 2^5x = 216

to solve for x, divide first both sides of the equation by 3

2^5x = 72

Apply log to both sides of the equation

log(2^5x) = log(72)

Apply logarithm property: log(xᵃ) = a log(x)

5x · log(2) = log(72)

divide both sides of the equation by 5 · log(2)

x = log(72) / (5 log(2))

Let´s check the solution:

3 ⋅ 2^5x = 216

3 · 2^5(log(72) / (5 log(2))) = 216

3 · 2^(log(72) / log(2)) = 216

3 · 72 = 216

216 = 216

Then x = log(72) / (5 log(2)) = 1.233985 is a solution of the equation

hello :

70y^8 + 30y^6 = 2 ( 35 y^8 + 15y^6)

the lenght is : 35 y^8

the width is : 15y^6

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.