All categories

3 years ago

27^x −1 = 9^3x−7 what is X

Mathematics

1 answer:

tigry1 [53]3 years ago

3 0

x is $\frac{11}{3}$

Step-by-step explanation:

Let us revise some rules of exponents

$(a^{n})(a^{n})=a^{m+n}$
$\frac{a^{m}}{a^{n}}=a^{m-n}$
$(a^{m})^{n}=a^{mn}$
$a^{m}=a^{n}$ , then m = n

∵ $27^{x-1}=9^{3x-7}$

- Factorize 27 and 9

∵ 27 = 3 × 3 × 3

∴ 27 = 3³

∵ 9 = 3 × 3

∴ 9 = 3²

Substitute them in the equation

∴ $(3^{3})^{x-1}=(3^{2})^{3x-7}$

- Use the third rule to simplify each side

∴ $(3)^{3x-3}=(3)^{6x-14}$

- Use the fourth rule

∵ The bases of the two sides are equal

∴ Their exponents are equal

∴ 3x - 3 = 6x - 14

- Subtract 6x from both sides

∴ -3x - 3 = -14

- Add 3 to both sides

∴ -3x = -11

Divide both sides by -3

∴ x = $\frac{11}{3}$

x is $\frac{11}{3}$

Learn more:

You can learn more about equations in brainly.com/question/4934417

#LearnwithBrainly

You might be interested in

Is 4/2 improper or proper

muminat

Answer:

Improper

Step-by-step explanation:

in order for it to be proper it must be written as 2

4 0

3 years ago

Read 2 more answers

By first calculating the size of angle LMN, calculate the area of triangle MNL. You must show all your working.

RSB [31]

Answer:

m(∠LMN) = 67.44°

Area of ΔMNL = 16.66 square units

Step-by-step explanation:

By applying Sine rule in the ΔLMN,

$\frac{\text{Sin}M}{\text{NL}}=\frac{\text{Sin}N}{\text{ML}}$

$\frac{\text{Sin}M}{7.2}}=\frac{\text{Sin}38}{\text{4.8}}$

SinM = $\frac{\text{Sin}38\times 7.2}{4.8}$

SinM = 0.9235

M = $\text{Sin^{-1}}(0.9235)$ $\text{Sin}^{-1} (0.9235)$

M = 67.44°

m(∠M) + m(∠N) + m(∠L) = 180°

67.44 + 38 + m(∠L) = 180°

m(∠L) = 180 - 105.44

m(∠L) = 74.56°

Area of ΔMNL = $\frac{1}{2}(\text{ML})(\text{NL})\text{Sin}(74.56)$

= $\frac{1}{2}(4.8)(7.2)(0.96391)$

= 16.66 square units

3 0

4 years ago

570 mL = ____ oz show step by step

Rzqust [24]

Solutions

570 ml to oz is: <span>19.27399 Ounces
</span>
= 19.27

3 0

4 years ago

Read 2 more answers

What does parallel mean? Can you give an example of things that are parallel?

klasskru [66]

Answer:

Defetion
meaning
number
meters

5 0

3 years ago

Read 2 more answers

A’s DJ service charges a $200 setup fee and $75 an hour after that.

Bogdan [553]

The total cost includes the setup cost + per hour cost.

Let, x represents the time and y represents the total cost.

$y=200+75x$ .... (1)

Let Y represent the cost for B's DJ service.

$y=125x$ .... (2)

a. Graphing both the equations give the intersection point (solution) as (4,500)

It means for 4 hours, the total cost of both the DJ's is same at $500.

b. Substitution Method.

Plug y = 125x in equation (1)

$125x= 200+75x$

$125x-75x=200$

$50x=200$

$x=4$

$y=125\times 4 =500$

Hence, the total cost for 4 hours in both the service is $500.

c. Addition method.

Multiply equation (2) by -1

$-y = -125x$ .... Equation (3).

Add euation (1) and equation (3)

$y+(-y) = 200+75x-125x$

$0=200-50x$

$50x=200, x=4$

$y=500$

Solution: For x = 4, y = 500 ( same as the previous two methods)

For x = 2, equation (1)

$y=200+(75\times 2) = 350$

For x = 2, equation (2)

$y= 125\times 2 =250$

Hence, for 2 hours, DJ B would be a better choice since it would charge $250.

For x = 6 hours, equation (1)

$y=200+(75\times 6) =650$

For x= 6, equation (2)

$y=125\times 6=750$

For 6 hours, DJ A would be better option since it charges $650 for 6 hours.

8 0

3 years ago