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
Flauer [41]
2 years ago
11

Solve log2(x + 5) + log2(x − 5) = log211.

Mathematics
2 answers:
OleMash [197]2 years ago
8 0

Answer:

x = 6

Step-by-step explanation:

log_2 ( x + 5 ) + log_2( ( x - 5 ) = log_2 11

Determined the define range.

log_2 ( x + 5 ) + log_2( ( x - 5 ) = log_2 (11), x ∈ ( 5, + ∞ )

We know that log_a ( b ) + log_a ( b ) = log_a( bc)

log_2 ( x + 5 ) ( x - 5 ) = log_2 ( 11).

log_2 ( ( x + 5 ) × ( x - 5 ) ) = log_2 ( 11).

Use indentity :- ( a + b ) ( a - b ) = a² - b².

log_2 ( x² + 25) = log_2 ( 11).

Since , the base of the logarithm are the same. set the arguments equal.

x² -<u> 25</u> = 11.

Move constant to the right-hand side and change their sign.

x² = 11 + 25

x² = 36.

Take square root of each side.

√x² = √36

x = ± 6

x = 6

x = -6, x ∈ ( 5, + ∞ )

Check if the solutions is in determine range.

x = 6

UkoKoshka [18]2 years ago
6 0

Answer:

x = 6

Step-by-step explanation:

log2(x + 5) + log2(x − 5) = log2 11.

We know that loga (b) + log a(c) = log a( bc)

log2(x + 5) (x − 5) = log2(11)

Multiply

log2(x^2 -25) = log2(11)

Raise each side to the power of 2

2^log2(x^2 -25) = 2^log2(11)

x^2 - 25 = 11

Add 25

x^2 -25 +25 = 25+11

x^2 = 36

Taking the square root of each side

x = ±6

But x cannot be negative because then the log would be negative in log2(x-5) and that is not allowed

x = 6

You might be interested in
Farmer Bill sold potatoes at the farm market. He sold a quarter to the first person, 4/9 of what was left to the second person,
oksian1 [2.3K]
10*9=90
3u->90
1u->30
4u->120 pounds
3 0
3 years ago
Read 2 more answers
A drawing of a tree and a wall are in the image below.
mina [271]

Answer:

<em>Choice B. 16 feet.</em>

<em>The height of the tree is 16 ft</em>

Step-by-step explanation:

<u>Similar Triangles</u>

Similar triangles have their corresponding side lengths proportional by a fixed scale factor.

We are given the drawings of a tree and a wall and it's assumed both triangles are similar. We need to find the scale factor and find the height of the tree.

Comparing the corresponding distances from the viewer to the base of the tree and the base of the wall, we can calculate the scale factor as 24/6=4.

Applying the same factor to the height of the model, we get the height of the tree is 4*4 = 16 ft.

Choice B. 16 feet

The height of the tree is 16 ft

6 0
3 years ago
According to this property, x + 0 = x.
Mumz [18]
The identity property of addition states that the sum of any number and 0 is the original number.

so...x + 0 = x would be the identity property of addition (also called the additive identity)
3 0
2 years ago
Read 2 more answers
Can someone plz help me
earnstyle [38]

Answer:

X=37.6 because the 90 degree angle plus the 52.4 equals 142.4 the subtract that from 180 then ta da.

6 0
3 years ago
5x^2-26x+5 factor the trinomial
ss7ja [257]
The factored form for this question is (5x-1)(x-5)
4 0
3 years ago
Other questions:
  • Factor the linear expression 5x-30
    11·1 answer
  • Can someone please help me I keep getting negative numbers for number 12
    14·1 answer
  • Simplify <br> 3 + (-8) -17
    6·2 answers
  • Use the table above to graph the function y = 2x - 2 with the domain (1,2,3).
    7·1 answer
  • On which number line are −6 and its opposite shown?
    8·1 answer
  • Please help due tomorrow
    5·2 answers
  • Eli and Claire work at a dry cleaners ironing shirts. Eli can iron 15 shirts per hour,
    15·1 answer
  • I need help pls this test is really hard
    11·1 answer
  • Which expression shows the sum of the polynomials with like terms grouped together?
    13·2 answers
  • What is the absolute value of<br> ?<br> Plot your answer on the number line.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!