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elena-s [515]
4 years ago
13

Write the expression as a single natural logarithm.3 ln x – 5 ln c

Mathematics
1 answer:
shtirl [24]4 years ago
4 0
The rules are ...
\Longrightarrow \ln(\frac{a}{b})=\ln(a)-\ln(b)
\Longrightarrow \ln(a^{b})=b\ln(a)

Your expression makes use of both these rules.
3\ln(x)-5\ln(c)=\ln(x^{3})-\ln(c^{5})=\ln \left( \dfrac{x^{3}}{c^{5}} \right)

Your single logarithm is ...
  \ln \left( \dfrac{x^{3}}{c^{5}} \right)
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How many times does 48 go into 80
anastassius [24]
1.666666666666667 to be exact, but rounded it is 1.66
3 0
3 years ago
Read 2 more answers
. The volume of a box is 405 cubic units. The length is x units, the width 4 units greater than the length, and the height is 9
lukranit [14]

Answer:

length = 5

width = 9

Step-by-step explanation:

V = lwh

let 'x' = length

let '4+x' = width

9 = height

405 = 9x(4+x)

405 = 36x + 9x²

this is a quadratic equation:  9x² + 36x - 405 = 0

factor out a 9 to get:

9(x² + 4x - 45) = 0

9(x-5)(x+9) = 0

one root is 5 and the other is -9

since distance cannot be negative we use 5 as the length and 9 is the width

3 0
3 years ago
If you were solving a system of equations and you came to a statement like 1 = 3, what do you know about the solution to the sys
noname [10]
<h2>Key Ideas</h2>
  • Systems of equations

<h2>Solving the Question</h2>

When both sides of the equal sign are equal, there are infinite solutions.

When you are able to isolate the variable, there is only one solution.

When the equation states an untrue expression, there is no solution.

1=3 is an untrue fact. Therefore, there would be no solutions to the system.

<h2>Answer</h2>

There is no solution

5 0
2 years ago
Can someone make 3 or more equations with 2 variables on both sides, in a fraction, integer, and decimal form?
Goryan [66]

hi it could be 3x+2=180 , 3/4x+19=189, 3.4x+12=100

8 0
4 years ago
What is the x-value in the solution to this system of linear equations?
ASHA 777 [7]

Answer:

  4

Step-by-step explanation:

The y-variable can be eliminated by adding 3 times the first equation to the second:

  3(2x -y) +(x +3y) = 3(11) +(-5)

  7x = 28 . . . .  simplify

  x = 4 . . . . . . . divide by 7

_____

Using Cramer's Rule, you can also find the x-value. The math is not so different.

  x = ((-1)(-5) -(3)(11))/(-1(1) -3(2)) = -28/-7 = 4

8 0
3 years ago
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