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Inessa [10]
3 years ago
12

Solve each of the following equations for x. 2^x − 1 = 0

Mathematics
1 answer:
AlekseyPX3 years ago
3 0

Answer:

The solution to the equation is x = 0

Step-by-step explanation:

Hi there!

First, let´s write the equation:

2ˣ - 1 = 0

To solve it for x, let´s add 1 to both sides of the equation:

2ˣ = 1

Apply log to both sides of the equation

log(2ˣ) = log(1)

Apply logrithm property: log(2ˣ) = x log(2)

x log(2) = log(1)

x log(2) = 0

x = 0

The solution is x = 0

Let´s check the solution:

2ˣ - 1 = 0

x = 0

2⁰ - 1 = 0

1 - 1  = 0

0 = 0

The solution is correct!

Have a nice day!

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Find the product. (a2 + 2a + 1)(a + 1) a. A2 + 3a + 2 b. A3 + 3a2 + 3a + 1 c. A3 + 2a 2 + a + 1 d. A3 + 3a2 + a + 1
olchik [2.2K]

 (a + 1)(a² + 2a + 1)

= a(a² + 2a + 1) + 1(a² + 2a + 1)

= a³ + 2a² + a   + a² + 2a + 1

= a³ + 3a² + 3a + 1

Answer: b

7 0
3 years ago
Write the product as a trinomial.
ddd [48]
1.  2r-5
2.  -21r-50
3.  4r-50
4.  14r+50
5.  19r-50
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3 years ago
Which ordered pair is a solution of the equation?<br> 7z -5 = 4y -6<br> Choose 1 answer:
ELEN [110]

Step-by-step explanation:

7z-5=4y-6

-4y=-6-7z+5

-4y=-1-7z

y=1/4+7/4z

y=7/4z+1/4

7z=4y-6+5

7z=4y-1

z=4/7y-1/7

3 0
2 years ago
Find the area of this rectangle <br> 13cm 8cm
castortr0y [4]

Answer:

104 cm squared

Step-by-step explanation:

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8 0
2 years ago
Suppose it takes 4 hours for a certain strain of bacteria to reproduce by dividing in half. If 70 bacteria are present to begin
Sauron [17]

Answer:

1 day: 4480

2 days: 8960

3 days: 13440

f^{-1}(x) = \sqrt{\frac{x -4}{4}} ---- function inverse

Step-by-step explanation:

Given

f(x) = 70 \cdot 64x

Solving (a): The amount present after 1 day.

Here, x =1

So:

f(1) = 70 \cdot 64*1= 4480

Solving (b): The amount present after 2 days.

Here, x =2

So:

f(2) = 70 \cdot 64*2= 8960

Solving (c): The amount present after 3 days.

Here, x = 3

So:

f(3) = 70 \cdot 64*2= 13440

Solving (d): The inverse function of:

f(x)= 4x^2 + 4

Replace f(x) with y

y= 4x^2 + 4

Swap x and y

x= 4y^2 + 4

Rewrite as:

4y^2 = x -4

Divide by 4

y^2 = \frac{x -4}{4}

Take square roots

y = \sqrt{\frac{x -4}{4}}

Replace y with function inverse

f^{-1}(x) = \sqrt{\frac{x -4}{4}}

6 0
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