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
Angelina_Jolie [31]
3 years ago
15

Solve the equation 3^(2x) -4*3^(x+1) + 27 = 0. use rules of exponents to change 3^(x+1)​

Mathematics
1 answer:
Leviafan [203]3 years ago
4 0

Answer:

\huge\boxed{x=1\ \vee\ x=2}

Step-by-step explanation:

3^{2x}-4\cdot3^{x+1}+27=0\\\\\text{use}\ (a^n)^m=a^{nm}\ \text{and}\ a^n\cdot a^m=a^{n+m}\\\\\left(3^x\right)^2-4\cdot3^x\cdot3^1+27=0\\\\\left(3^x\right)^2-12\cdot3^x+27=0\\\\\text{substitute}\ 3^x=t>0\\\\t^2-12t+27=0\\\\t^2-3t-9t+27=0\\\\t(t-3)-9(t-3)=0\\\\(t-3)(t-9)+0\iff t-3=0\ \vee\ t-9=0\\\\t-3=0\qquad\text{add 3 to both sides}\\\boxed{t=3}\\\\t-9=0\qquad\text{add 9 to both sides}\\\boxed{t=9}

\text{We return to substitution:}\\\\3^x=t\\\\3^x=3\ \vee\ 3^x=9\\\\3^x=3^1\ \vee\ 3^x=3^2\\\\\boxed{x=1}\ \vee\ \boxed{x=2}

You might be interested in
Tanx cscx= 1/f(x)<br>simplify and write the trigonometric expression in terms of sine and cosine​
Aleonysh [2.5K]

Answer:

f(x) = cos(x)

Step-by-step explanation:

tanx cscx = (sinx/cosx) * (1/sinx) = 1/cosx

1/f(x) = 1/cosx

f(x) = cos(x)

5 0
3 years ago
I need help, plzzzzzzzzzz 10 points
bazaltina [42]
Add and convert it into a mixed fraction
8 0
2 years ago
Read 2 more answers
A line crosses the coordinates (-2,-5) and (3,5). What is the slope of the line?<br> 1
Talja [164]

Answer:

(y2-y1)/(x2-x1)

(5+5)/(3+2)

10/5

2 is the slope

7 0
3 years ago
Please help! Which are acceptable names for the line?
serg [7]
'B' and 'D' are correct.
'C' isn't, and we don't know about 'A' because you left it out.
6 0
3 years ago
Read 2 more answers
Can someone help mme
Vanyuwa [196]

Answer:

ok this is that and that is this.hope this helps

5 0
2 years ago
Other questions:
  • Confused on "their sum is to the sum of their squares as 7 is to 50." Help me put this in a equation please
    9·2 answers
  • 9(5x + 1) ÷ 3y
    14·1 answer
  • Explain why you usually need to use to find the volume of a cylinder.
    6·2 answers
  • An airplane flies at a speed of 474 miles per hour. How many miles does the plane fly in 5 hours?
    5·2 answers
  • Which is a rational number?<br> √6<br> √36/16<br> √16/6<br> √36/6
    7·1 answer
  • D. How many dozen doughnuts are there in 46.2 doughnuts?
    11·2 answers
  • Write each number in standard notation
    8·2 answers
  • Estimate 2,525 ÷ 64<br> nononononononnow
    13·2 answers
  • Directions:
    15·1 answer
  • Find value of x please
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!