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Fittoniya [83]
2 years ago
13

3^x= 3*2^x solve this equation​

Mathematics
1 answer:
kompoz [17]2 years ago
8 0

In the equation

3^x = 3\cdot 2^x

divide both sides by 2^x to get

\dfrac{3^x}{2^x} = 3 \cdot \dfrac{2^x}{2^x} \\\\ \implies \left(\dfrac32\right)^x = 3

Take the base-3/2 logarithm of both sides:

\log_{3/2}\left(\dfrac32\right)^x = \log_{3/2}(3) \\\\ \implies x \log_{3/2}\left(\dfrac 32\right) = \log_{3/2}(3) \\\\ \implies \boxed{x = \log_{3/2}(3)}

Alternatively, you can divide both sides by 3^x:

\dfrac{3^x}{3^x} = \dfrac{3\cdot 2^x}{3^x} \\\\ \implies 1 = 3 \cdot\left(\dfrac23\right)^x \\\\ \implies \left(\dfrac23\right)^x = \dfrac13

Then take the base-2/3 logarith of both sides to get

\log_{2/3}\left(2/3\right)^x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x \log_{2/3}\left(\dfrac23\right) = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(3^{-1}\right) \\\\ \implies \boxed{x = -\log_{2/3}(3)}

(Both answers are equivalent)

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Given the functions f(x) = 3(0.56)^x and g(x) = 6(4)^x
rodikova [14]
A)  f(x) is decreasing because the base is less than 1.
      0.56 is close to 0.5, so its like saying that you are taking half each time, therefore the value is getting smaller.

g(x) is increasing because the base is greater than 1.
you are multiplying by 4 each time, making the value bigger.


B )  The y-intercept is where x=0.
      Anything to the '0' power is 1. Therefore the y-intercept is equal to the coefficient in front of each function.
    f(x) = 3 ,   g(x) = 6


C)  Just plug in x=4 to each function in a calculator.
 f(4) = 0.295
g(4) = 1536
7 0
3 years ago
How do you do 1/4 (16x+20)-7x
Ira Lisetskai [31]
Distribute the 1/4:
1/4(16x) + 1/4(20) - 7x

Do the multiplication:
1/4(16x) = 16x/4 = 4x
1/4 (20) = 20/4 = 5

Now you have:
4x + 5 - 7x = 0

Combine like terms (4x and -7x):
-3x + 5 = 0

Subtract 5 from both sides:
-3x = -5

Divide by -3:
x = -5/-3 = 5/3

Answer:
x= 5/3
6 0
3 years ago
. Use the statistical features of your calculator to find the mean and the standard deviation to the nearest tenth of a data set
uysha [10]

Answer:

Mean = 1.9

Standard deviation = 0.6

Step-by-step explanation:

The Mean is calculate by the formula:

Mean = \frac{\text{Sum of all the observation}}{\text{Total number of observation}}

⇒ Mean = \frac{24.9+24.7+24.7+23.4+27.9}{5} = 1.85

Thus Mean to the nearest tenth is 1.9

Standard Deviation is the square root of sum of square of the distance of observation from the mean.  

Standard deviation(\sigma) = \sqrt{\frac{1}{n}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}} }

where, \bar{x} is mean of the distribution.

Putting all values in the formula, We get

Standard Deviation = 0.597 ≈ 0.6

6 0
3 years ago
Help me I need help ASAP will <br> Give BRAINLIEST
makvit [3.9K]

Answer:

real numbers: all

rational: all but pi

Integers: 20,-9

Whole, 20,-9, radical 16

Natural: 20

Irrational: pi

Step-by-step explanation:

5 0
3 years ago
Classify each number as rational or irrational. Drag the choices into the boxes to correctly complete the table.
Alex17521 [72]

Answer:

3 = irrational

-1/16 = rational

0 = rational

2 =irrational

7 0
3 years ago
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