1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Gemiola [76]
1 year ago
6

20" id="TexFormula1" title="4 {}^{x } + 6 {}^{x} = 9 {}^{x} " alt="4 {}^{x } + 6 {}^{x} = 9 {}^{x} " align="absmiddle" class="latex-formula">
please find x. and with explanation thanks ​
Mathematics
1 answer:
Nookie1986 [14]1 year ago
5 0

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.

<h3>How to find x?</h3>

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:

brainly.com/question/11832081

#SPJ1

You might be interested in
Convert –18° to radians. Negative 10 pi radians Negative StartFraction 10 Over pi EndFraction radians Negative StartFraction 1 O
REY [17]

Answer:

negative pie/10 radians

Step-by-step explanation:

d on edg

6 0
2 years ago
Read 2 more answers
$490 at 2.1% compounded<br> quarterly for 6 months
Lostsunrise [7]
The answer is 892$ , i hope this helps u
4 0
2 years ago
The answer bNamamakakKkKkkKk
skad [1K]
That is really easy how don't you know
4 0
2 years ago
4. A line with a slope of -2 passes
Shalnov [3]

Answer:

y=-2x+5..…...........

6 0
2 years ago
1. Find the domain and range
andre [41]

1. Find the domain and range

{(0, 0), (1,−1),(2,−4),(3,−9),(4,−16)(1,−1),(2,−4),(3,−9),(4,−16)

Domain:{0,1,2,3,4}

Range: {0,−1,−4,−9,−16}

2. Suppose f(x)=2x−5. Find the value of f(3)

1 is your answer

3. Write an equation of the line in standard form with the given slope through the given point.

Slope = -3 and (0,0)

y=mx+b.

y=−3x

4. For the direct variation, find the constant of variation. Then find the value of y when x = 2

Y = 4, x= 0.5

5. Write an equation of the line with the given slope and y-intercept. Use slope – intercept form.

M = 3, b = 5

m=\frac{2}{b-m}

6 0
2 years ago
Other questions:
  • 1kg= 2.2 pounds<br> Change 44 pounds in kg
    13·1 answer
  • if 1 and a half inch represents 50 miles, how many inches are needed to represent 225 miles ? show all of your work
    5·2 answers
  • Seven years less than 13 times the age, written algebraically.
    12·1 answer
  • At Keller's Bike Rentals, it costs 42$ to rent a bike for 8 hours. How many hours of bike use does a customer get per dollar? ro
    13·1 answer
  • Suppose that f(x)=x^3 and g(x)=-2^3-7 which statement best compares the graph of g(x) with the graph of f(x)
    13·1 answer
  • What is the completely factored form of this expression?
    8·1 answer
  • At a local restaurant, the health inspector visits every 7 days, and the fire inspector visits every 12 days.
    14·1 answer
  • Y=-4x+2<br> y = 6.x-8<br><br> I don’t understand
    15·1 answer
  • The point (3,-7) lies on a circle and the center of the circle is at (-2,-7). What is the equation of this circle
    10·1 answer
  • Please help me and show work on a piece of paper​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!