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3 years ago

How do you solve 3^2x=81

Mathematics

2 answers:

Jobisdone [24]3 years ago

7 0

Answer:

x=ln(81) over 2ln(3)

Step-by-step explanation:

Using ln as its base thing instead of log and the formula usually is log over log. Plus you have to bring down the power that way.

qwelly [4]3 years ago

4 0

Answer:

x=2

Step-by-step explanation:

3^2x = 81

3^2x = 3^4

Compare powers

2x = 4

x = 2

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Jada was measuring the dimensions of her new closet. The area of the closet is 8 1/6 square feet and the width of the closet is

Vitek1552 [10]

Answer: 2 1/3 feet

Step-by-step explanation:

Area of closet = 8 1/6 feet ²

Width of the closet = 3 1/2 feet

Length of the closet = Unknown

We should note that:

Area = Length × Width

Length = Area / Width

Length = 8 1/6 ÷ 3 1/2

= 49/6 ÷ 7/2

= 49/6 × 2/7

= 7/3

= 2 1/3 feet

The length is 2 1/3 feet

6 0

3 years ago

Minimum Average Cost

Dahasolnce [82]

Answer:

a) $\bar{C}(x)=\dfrac{100}{x}+25-120\dfrac{lnx}{x}$

b) $\bar{C}(x)=5.81$

Step-by-step explanation:

Given that

C = 100 + 25 x - 120 ln x ,x ≥ 1.

The average cost function given as

$\bar{C}(x)=\dfrac{C(x)}{x}$

$\bar{C}(x)=\dfrac{100 + 25 x - 120 \ln x}{x}$

$\bar{C}(x)=\dfrac{100}{x}+25-120\dfrac{lnx{x}$

Therefore

$\bar{C}(x)=\dfrac{100}{x}+25-120\dfrac{lnx}{x}$

To find average minimum cost

$\bar{C}(x)=\dfrac{100}{x}+25-120\dfrac{lnx}{x}$

$\dfrac{d\bar{C}(x)}{dx} = -\dfrac{100}{x^2} +0-120\times \dfrac{1-lnx}{x^2}$

$0 = -\dfrac{100}{x^2} +0- 120\times \dfrac{1-lnx}{x^2}$

100 + 120 (1-lnx) = 0

$lnx=\dfrac{220}{120}$

ln x =1.833

$x=e^{1.833}$

x=6.25

$\bar{C}(x)=\dfrac{100}{6.25}+25-120\dfrac{ln6.25}{6.25}$

$\bar{C}(x)=5.81$

6 0

4 years ago

Two arcades have different pricing structures. Arcade A costs $5 to enter and $0.60 per game. Arcade B costs $7 to enter and $0.

WARRIOR [948]

Answer:

10 games

Step-by-step explanation:

Let C be cost and x be number of games

Arcade A: C = 5 + 0.6x

Arcade B: C = 7 + 0.4x

for both arcades to be the same price, Both C's must be equal, hence we equate the right side of both equations:

5 + 0.6x = 7 + 0.4x (subtract 5 fromboth sides)

0.6x = 7 + 0.4x - 5

0.6x = 2 + 0.4x (subtract 0.4x from both sides)

0.6x - 0.4x = 2

0.2x = 2 (divide both sides by 0.2)

x = 2 / (0.2)

x = 10

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3 years ago

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Oliga [24]

The answer should be c

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4 years ago

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MrRa [10]

The plane PRS passes through the points P, R and S. So it contains the line RS. Also the plane QRS passes through the points Q, R and S. So it contains the line RS as well. Since both the planes contain the line RS, the line RS must be the intersection of plane PRS and QRS

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3 years ago