Question 19: Solve for X.

<img src="https://tex.z-dn.net/?f=4%20%20%20%7B%7D%5E%7Bx%20%7D%20%20%2B%206%20%7B%7D%5E%7Bx%7D%20%3D%209%20%7B%7D%5E%7Bx%7D%20%

Nookie1986 [14]

So, the value of x is 1.19

The question is an exponential equation

<h3>What is an exponential equation?</h3>

An exponential equation is a mathematical expression between two quantities in which one variable is raised to a power of the other variable.

Since $4^{x} + 6^{x} = 9^{x}$ ,

Dividing through by 4ˣ, we have

$\frac{4^{x} }{4^{x} } + \frac{6^{x} }{4^{x} } = \frac{9^{x} }{4^{x} } \\1 + (\frac{6}{4})^{x} } = (\frac{9}{4})^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3^{2} }{2^{2} })^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3}{2})^{2x} }$

Let y = (3/2)ˣ

So,

1 + y = y²

y² - y - 1 = 0

Using the quadratic formula to find y,

$y = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}$

where a = 1 b = -1 and c = -1

Substituting the values of the variables into the equation, we have

$y = \frac{-(-1) +/- \sqrt{(-1)^{2} - 4\times 1 \times (-1)} }{2\times 1}\\= \frac{1 +/- \sqrt{1 + 4} }{2}\\= \frac{1 +/- \sqrt{5} }{2}\\= \frac{1 - \sqrt{5} }{2} or \frac{1 + \sqrt{5} }{2}\\= \frac{1 - 2.236}{2} or \frac{1 + 2.236}{2}\\= \frac{- 1.236}{2} or \frac{3.236}{2}\\= -0.618 or 1.618$

Since y = (3/2)ˣ

Takung logarithm of both sides, we have

㏒y = ㏒(3/2)ˣ

㏒y = x㏒(3/2)

x = ㏒y/㏒(3/2)

x = ㏒y/㏒1.5

Since we do not have logarithm of a negative number, we use y = 1.618.

So, x = ㏒y/㏒1.5

x = ㏒1.618/㏒1.5

x = 0.2090/0.1761

x = 1.19

So, the value of x is 1.19

Learn more about exponential equation here:

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5 0

10 months ago

Use the properties of rational exponents to simplify 6/6 1/4

Alexeev081 [22]

Answer:

one

Step-by-step explanation:

Use the properties of rational exponents

6 0

2 years ago

In 2000 South Dakota had a population of 754,844. The number of people in South Dakota increased by 7.9% in 2010. What is South

Novay_Z [31]

814,180. Hope I helped. If i didn't I am sos sorry. I would take 7.9 or .079 to 754,844 to get your number.

6 0

2 years ago

I need help for math plz :(

Lemur [1.5K]

Answer:

Option D

Step-by-step explanation:

Set of data in terms of ordered pairs represents a function when output value of each input value is different.

Option A

Since, for every value of x there is a different value of y, it's a function.

Option B

In each ordered pair, for every value of x there is a different value of y.

Therefore, it's a function.

Option C

From the given graph, for every value of x there is a different value of y.

Therefore, it's a function.

Option D

From the given set of ordered pairs we find for x = 1 there are two values of y (y = 4 and 3).

Therefore, the given set of ordered pairs doesn't represent a function.

Option D is the answer.

6 0

2 years ago

4. Find the measure of each interior angle of a regular polygon with 12 sides.

professor190 [17]

For any polygon the sum of the exterior angles is 360. Since The polygon is regular divide 360 by 12 to get the exterior angle measure. Interior and exterior angles are supplemental so subtract the exterior angle measure from 180.<span>
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6 0

2 years ago

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