All categories

2 years ago

(1/2)^(x-3) = (1/4)^(x-5) Solve for x using logs

Mathematics

1 answer:

inn [45]2 years ago

5 0

(X-3)*log(1/2)=(x-5)*log(1/4)
X-3=(log(1÷4)÷log(1÷2))*(x-5)
X-3=2(x-5)
X-3=2x-10
X-2x=3-10
-x=-7
X=7

You might be interested in

you invest $2,000 in a stock plan and another $2,000 in a savings account the stock plan decreases 7% the first year and gains 1

Dahasolnce [82]

After calculating the stock and savings account total I found out that the difference in earning between them is $104.738.

8 0

3 years ago

Read 2 more answers

Three poultry farms B1, B2, and B3 supply chicken eggs to the same local market. The market performs some quality testing on the

ipn [44]

Answer:

a. 0.58

b. 0.78

Step-by-step explanation:

a. The probability of egg come from B1 or B2

P(B1) = 3000/10000 = 0.3

P(B2) = 4000/10000 = 0.4

P(P1 ∪ B2) = 0.3 + 0.4 -(0.3)(0.4)

P(P1 ∪ B2) = 0.7 - 0.12

P(P1 ∪ B2) = 0.58

b. The probability that the market received an egg that is acceptable

P(received an egg that is acceptable) = P(B1 acceptable) + P(B2 acceptable) + P(B3 acceptable)

P(received an egg that is acceptable) = 0.80*3000 + 0.90*4000 + 0.60*3000 / 10000

P(received an egg that is acceptable) = 2400 + 3600 + 1800 / 10000

P(received an egg that is acceptable) = 7800 / 10000

P(received an egg that is acceptable) = 0.78

4 0

3 years ago

Coleman uses his graphing calculator to find all of the solutions to the equation shown below.

Phoenix [80]

Answer:

The correct option is;

D. x = -1.38 and 0.82

Please find attached the combined function chart

Step-by-step explanation:

The given equation is x³ + 3 = -x⁴ + 4

Plotting the equation using Excel, we have;

f(x) = x³ + 3, h(x) = -x⁴ + 4

x f(x) h(x)

-1.4 0.256 0.1584

-1.39 0.314381 0.26699

-1.38 0.371928 0.373261

-1.37 0.428647 0.477246

-1.36 0.484544 0.57898

Which shows an intersection at the point around -1.38

x f(x) h(x)

0.77 3.456533 3.64847

0.78 3.474552 3.629849

0.79 3.493039 3.610499

0.8 3.512 3.5904

0.81 3.531441 3.569533

0.82 3.551368 3.547878

0.83 3.571787 3.525417

Which shows the intersection point around 0.82

Therefore, the correct option is x = -1.38 and 0.82

From the graphing calculator the intersection point is given as

x = -1.3802775691 and 0.81917251339.

8 0

2 years ago

Let y in the form of a + ib, where a and b are real numbers, be the cubic roots of a complex number z 20, where z =2 4+i3. Find

GalinKa [24]

The possible values of a + b are 0.89, 3.01 and -3.9

<h3>How to determine the value of a + b?</h3>

The given parameters are:

y = a + ib

z = 24 + i3

Where:

y = ∛z

Take the cube of both sides

y³ = z

Substitute the values for y and z

(a + ib)³ = 24 + i3

Expand

a³ + 3a²(ib) + 3a(ib)² + (ib)³ = 24 + i3

Further, expand

a³ + i3a²b + i²3ab² + i³b³ = 24 + i3

In complex numbers;

i² = -1 and i³= -i

So, we have:

a³ + i3a²b + (-1)3ab² -ib³ = 24 + i3

Further expand

a³ + i3a²b - 3ab² - ib³ = 24 + i3

By comparing both sides of the equation, we have:

a³ - 3ab² = 24

i3a²b - ib³ = i3

Divide through by i

3a²b - b³ = 3

So, we have:

a³ - 3ab² = 24

3a²b - b³ = 3

Using a graphing tool, we have:

(a,b) = (-1.55, 2.44), (2.89,0.12) and (-1.34,-2.56)

Add these values

a + b = 0.89, 3.01 and -3.9

Hence, the possible values of a + b are 0.89, 3.01 and -3.9