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
ale4655 [162]
2 years ago
10

Is there an error in the work and is the answer extraneous? if so why?​

Mathematics
1 answer:
Thepotemich [5.8K]2 years ago
8 0

Answer:

x = 4

Step-by-step explanation:

log₃[1 + log₃(2ˣ - 7)] = 1

log₃[1 + log₃(2ˣ - 7)] = log₃(3)

1 + log₃(2ˣ - 7) = 3

log₃(2ˣ - 7) = 2

log₃(2ˣ - 7) = log₃(3)²

2ˣ - 7 = 9

2ˣ = 9 + 7

2ˣ = 16

2ˣ = 2⁴

x = 4

By putting x = 4 in the original equation,

log₃[1 + log₃(2⁴ - 7)] = 1

log₃[1 + log₃(16 - 7)] = 1

log₃[1 + log₃(9)] = 1

log₃[1 + log₃(3)²] = 1

log₃[1 + 2] = 1

log₃[3] = 1

1 = 1

Therefore, x = 4 is not the extraneous solution and there is no error in your answer.

You might be interested in
Which inequality is equivalent to x-6/x+5≥x+7/x+3?
yawa3891 [41]
To find equivalent inequalities you have to work the inequality given.

The first step is transpose on of sides to have an expression in one side and zero in the other side:

  x - 6        x + 7
--------- ≥  --------
  x + 5       x + 3

=>

  x - 6          x + 7
--------- -  --------   ≥ 0
  x + 5       x + 3

=>

 (x - 6) (x + 3) - (x + 7) (x + 5)
--------------------------------------- ≥ 0
          (x + 5) (x + 3)

=>

 x^2 - 3x - 18 - x^2 - 12x - 35
--------------------------------------- ≥ 0
         (x + 5) (x + 3)

           15x + 53
-     -------------------   ≥ 0
       (x + 5) (x + 3)

That is an equivalent inequality. Sure you can arrange it to find many other equivalent inequalities. That is why you should include the list of choices. Anyway from this point it should be pretty straigth to arrange the terms until making the equivalent as per the options.
4 0
3 years ago
Read 2 more answers
maria wanted to invest $10,000 at the bank. she invested part of her money in a cd account paying 2.1% simple interest and inves
tangare [24]

Answer:I = ?, P = $500, r = 6%, t = 3 years

Step-by-step explanation:

6 0
3 years ago
Find the Volume. Can someone explain how they did it. thank you
hodyreva [135]
6 x 5 x 7 = 210
The volume formula is length x width x height :)
4 0
3 years ago
Read 2 more answers
What is2/3 divided by 4/5
Sloan [31]
The answer to this question is 5/6
8 0
3 years ago
Read 2 more answers
Please help with this problem!!
hodyreva [135]

The answer is A because the two lines are equal

8 0
3 years ago
Other questions:
  • -14+6b+7-2b=1+5b<br> someone help me with this please
    7·2 answers
  • Use the indicated x-values on the graph of y = f(x) to find the following.
    6·1 answer
  • If Chris has 2 times as many nickels as quarters and they have a combined value of 210 cents, how many of each coin does he have
    15·1 answer
  • What is the value of a? Enter your answer in the box. a = A right triangle with base labeled as 20. The hypotenuse is labeled as
    5·1 answer
  • Joe does push-ups, sit-ups, and jumping jacks. He does these in a different order every day. How many different orders are possi
    7·2 answers
  • What is 7/15 as a decimal
    11·1 answer
  • Triangle ABC is rotated 180° using the origin as the center of rotation.
    13·1 answer
  • What is the first step in solving this problem:<br> -12 ÷ 6 (-3) + 8<br> WILL GIVE BRANLIEST
    14·2 answers
  • A Taxi company charges $2.75 flat rate in addition to $0.85 per mile. Pepe has no more than $10 tospend on a ride. Write an ineq
    8·1 answer
  • 2.5 kg cost £1.40<br><br>work out the cost of 4.25kg
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!