All categories

3 years ago

What is the exact solution to the equation 4^5x=3^(x-2) list the steps to get the answer

Mathematics

1 answer:

scoray [572]3 years ago

6 0

Answer: x = -0.377

Step-by-step explanation:

We have the equation:

4^(5*x) = 3^(x - 2)

Now we can use the fact that:

Ln(A^x) = x*Ln(A)

Then we can apply Ln(.) to both sides of the equation to get:

Ln(4^(5*x)) = Ln(3^(x - 2))

(5*x)*Ln(4) = (x - 2)*Ln(3)

(5*x)*Ln(4) - x*Ln(3) = -2*Ln(3)

x*(5*Ln(4) - Ln(3)) = -2*Ln(3)

x = -2*Ln(3)/(5*Ln(4) - Ln(3)) = -0.377

You might be interested in

A machine takes 5.4 hours to make 9 parts. At that rate how many parts can the machine make in 25.8 hours

Sliva [168]

$\frac{5.4}{9} = \frac{25.8}{x}$ Cross multiply.

5.4x=9*25.8

5.4x=232.2 Divide both sides by 5.4

x=43

4 0

3 years ago

Read 2 more answers

Determine the distance between point (x1, y1) and point (x2, y2), and assign the result to point distance. the calculation is: d

Ronch [10]

we are given two points as

(1.0, 2.0) and (1.0, 5.0)

so,

(x1, y1)= (1.0 , 2.0)

(x2, y2)= (1.0 , 5.0)

x1=1 , y1=2

x2=1 , y2=5

now, we can use distance formula

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

now, we can plug values

and we get

$d=\sqrt{(1-1)^2+(5-2)^2}$

$d=\sqrt{(0)^2+(3)^2}$

$d=\sqrt{(3)^2}$

$d=3$

so, distance between points is 3...........Answer

5 0

3 years ago

I need help asap!!!

valentina_108 [34]

The answer is (7,6)

This is because a midpoint is in the exact middle, meaning that both sides are an equal distance away. You can find this by fining the difference between the two corresponding coordinates then adding that difference to the midpoint and that will give you your other endpoint.

Hope this helped !!

7 0

2 years ago

If 0.5% of a number is 250, find the number

kaheart [24]

0.5% or 1/2% of say "x" is 250, whilst "x" is the 100%.

$\begin{array}{ccll} \%&amount\\ \cline{1-2} \frac{1}{2}&250\\[1em] 100&x \end{array}\implies \cfrac{~~ \frac{1}{2}~~}{100}=\cfrac{250}{x}\implies \cfrac{1}{200}=\cfrac{250}{x}\implies x = 50000$

6 0

2 years ago

Read 2 more answers

In a class of 30, students play either football or basketball (or both). If 21 students play football and 24 students play only

Murljashka [212]

Answer:

6 play both

Step-by-step explanation:

30-24=6

4 0

3 years ago

Read 2 more answers