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Mumz [18]
3 years ago
15

Solve for x, log(5x-5)=log(2x+3)+log(15)

Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
5 0
\log(5x-5)=\log(2x+3)+\log15\\
\log(5x-5)=\log[15(2x+3) ], \text{ because } \log(ab)=\log a+\log b\\
\log(5x-5)=\log(30x+45)\\
5x-5=30x+45, \text{ because } (\log x=\log y\rightarrow x=y.)\\
-25x=50\\
\text{Then } x=-2.
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On a coordinate plane, a line is drawn from point J to point K. Point J is at (1, negative 10) and point K is at point (7, 2). W
nevsk [136]

Answer:

The point that divides the directed line segment from J to K into a ratio of 5:1 is (6, 0), its y-coordinate is 0.

Step-by-step explanation:

We take J as point one, with coordinates (x1, y1) = (1, -10) and K as point two with coordinates (x2, y2) = (7, 2)

The "run" is the change in the x-coordinates:  x2 - x1 = 7 - 1 = 6

The "rise" is the change in the y-coordinates: y2 - y1 = 2 - (-10) = 12

For the partition ratio, let the numerator = a and the denominator = b.

The coordinates of the point P (x, y), which divides the directed line segment from J to K into a ratio of 5:1 is:

x = x1 + a/(a+b)*run

x = 1 + 5/(5+1)*6

x = 6

y = y1 + a/(a+b)*rise

y = -10 + 5/(5+1)*12

y = 0

5 0
3 years ago
Slove the system<br> Of Linear Eqitions by<br> Elimination <br> 3x-y=0<br> 2x+y=-10
Arlecino [84]

Answer:

<em>(-2, -6)</em>

Step-by-step explanation:

Given the simultaneous equation

3x-y=0 ... 1

2x+y=-10 ... 2

Add both equations to eliminate y

3x + 2x = 0 - 10

5x = -10

x = -10/5

x = -2

Substitute x = -2 into 1

3(-2)- y = 0

-6 - y = 0

-y = 0+ 6

-y = 6

y = -6

<em>Hence the coordinate (x, y) is (-2, -6)</em>

5 0
3 years ago
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