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ss7ja [257]
3 years ago
10

How do you solve this multi-step equation involving natural logarithms? ln(x-3)-ln5=1

Mathematics
1 answer:
sasho [114]3 years ago
5 0

Answer:

Step-by-step explanation:

Step 1, when  subtracting logs with the same base you can rewrite it with one log and the argument becomes division...

ln(x - 3) - ln 5 = 1 becomes...

            ln [ (x - 3)/5 ]  = 1

Step 2, rewrite the by putting into exponential form...ln has a base of e, so we get..

    e^1 = (x -3)/5

Now solve...

  e = (x - 3)/5

       5e = x - 3

             5e + 3 = x

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Triangles IJK and LMN are similar. Find y using proportions. Explain and show all your steps.
Deffense [45]

Triangles IJK and LMN are similar. Then, the proportion between their similar sides must be equal. That is:

IJ/ML = JK/MN = IK/LN

where:

IJ = x

JK = 54

IK = y

MN = 42

ML = 28

NL = 35

In order to find the value of y, you consider the equation JK/MN = IK/LN, and solve for y, just as follow

JK/MN = IK/LN replace by the values

54/42 = y/35 multiply both sides by 35

(54/42)(35) = y

45 = y

Hence, y = 45

4 0
1 year ago
3,000 kilometers with three friends 6 liters of gas per 100 kilometers and gas costs 1.20 per liter
dimaraw [331]
3000:100×6=180 liters
180×1,2=216 $
216÷6=36$/friend
4 0
3 years ago
Explain how you would graph the line containing a slope of –1/5 that goes through the point (1,–4).
Anettt [7]
Slope = -1/5
Coordinate = (1, -4)

We know, y - y1 = m(x - x1)
y + 4 = -1/5 (x - 1)
y + 4 = -1/5x + 1/5
y = -1/5x -19/5

When, x = 1, y = -1/5(1) - 19/5 = -20/5 = -4
x = 2, y = -1/5(2) - 19/5 = -21/5
x = 3, y = -1/5(3) - 19/5 = -22/5

Here, Your Coordinates would be: (0, -4), (1, -21/5), (2, -22/5)
Mark them & draw the lines. Graph is done!

Hope this helps!
5 0
3 years ago
Read 2 more answers
Solve the matrix equation below. What is the value of x in the new matrix?
andrew11 [14]

The new matrix that is formed by the 3A + B is given below. Then the value of x is 102.

\begin{bmatrix} w & z \\y & z \\\end{bmatrix} =  \begin{bmatrix} 46 & 102 \\15 & -2 \\\end{bmatrix}

<h3>What is the matrix?</h3>

A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The a_{ij } element in a matrix, such as M, refers to the i-th row and j-th column element.

The matrices are given below.

\rm A = \begin{bmatrix}9 & 27 \\0 & 6 \\\end{bmatrix}\\\\\\B = \begin{bmatrix}19 & 21 \\15 & -20\\\end{bmatrix}

Then the new matrix is given as 3A + B. Then we have

\rm 3A + B =\begin{bmatrix} w & z \\y & z \\\end{bmatrix}\\\\\\3A + B =3 \times  \begin{bmatrix}9 & 27 \\0 & 6 \\\end{bmatrix} + \begin{bmatrix}19 & 21 \\15 & -20\\\end{bmatrix}\\\\\\3A + B = \begin{bmatrix}27& 81\\0 & 18\\\end{bmatrix} + \begin{bmatrix}19 & 21 \\15 & -20\\\end{bmatrix}\\\\\\3A + B = \begin{bmatrix} 46 & 102 \\15 & -2 \\\end{bmatrix}

More about the matrix link is given below.

brainly.com/question/9967572

#SPJ1

5 0
3 years ago
8=t/-3+4 help me please
Fittoniya [83]

*RE-EDITED

8=\frac{t}{-3}+4 \\ \\ 8-4=\frac{t}{-3} \\ \\ 4=\frac{t}{-3}\\ \\ 4(-3)=t=-12

Hope that helps!

4 0
3 years ago
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