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
Furkat [3]
3 years ago
9

Please Hurry! What is the solution to log2_(9x)-log2_3=3?

Mathematics
2 answers:
Gemiola [76]3 years ago
7 0

Answer:

\log _2\left(9x\right)-\log _2\left(3\right)=3 : x = \frac{8}{3}

Decimal:

x = 2.66666...

Step-by-step explanation:

\log _2\left(9x\right)-\log _2\left(3\right)=3

Add log _2\left(3) to both sides:

\log _2\left(9x\right)-\log _2\left(3\right)+\log _2\left(3\right)=3+\log _2\left(3\right)

Simplify:

\log _2\left(9x\right)=3+\log _2\left(3\right)

Use the logarithmic definition: If \log _a\left(b\right)=c\:\mathrm{then}\:b=a^c

\log _2\left(9x\right)=3+\log _2\left(3\right)\quad \Rightarrow \quad \:9x=2^{3+\log _2\left(3\right)}

9x=2^{3+\log _2\left(3\right)}

Expand 2^{3+\log _2\left(3\right)} : 24

9x=24

Solve: 9x=24 : x = \frac{8}{3}

x = \frac{8}{3}

Verify solutions: x = \frac{8}{3}  : True

The solution is:

x=\frac{8}{3}

Hope I helped. If so, may I get brainliest and a thanks?

Thank you, have a good day! =)

brilliants [131]3 years ago
6 0

Answer:

log_{2}(9x)  - log_{2}(3) = 3 \\ 3 =  log_{2}(8) or log_{2}( {2}^{3} )  \\  log_{2}( \frac{9x}{3} )  = log_{2}(8) \\  \frac{9x}{3}  = 8 \\ 9x = 8 \times 3 \\ 9x = 24 \\ x =  \frac{24}{9}  \\ x =  \frac{8}{3}  \\ x = 2 \times \frac{2}{3}

You might be interested in
Find g(f(-1)).<br> gf-1)) =(
Licemer1 [7]

Answer:

sorry i dont know this one! :)

it does not make any scene.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Is 2,710,506 divisible by 8? ​
Lubov Fominskaja [6]

Answer:

no

Step-by-step explanation:

3 0
3 years ago
PLEASE HELPPP MEEEEE
Blizzard [7]

Answer:

OMH OKOK WAIT IMMA TRY TO FIND IT

7 0
3 years ago
you put $400 in an account. the account earns $18 simple interest in 3 years. what is the annual interest​
nadya68 [22]

Answer:

$6

Step-by-step explanation:

divide 18 into three

18÷3=6

8 0
3 years ago
Light travels at 3.0×10^8 kilometers how far does light travel in five minutes
34kurt
Just have a very grate day
8 0
3 years ago
Other questions:
  • An area of 4 square yards is equal to 36 square feet. Using this information, 10 square yards is equal to how many square feet?
    7·2 answers
  • How did you figure out the answers ? how did you work it out ?
    6·1 answer
  • Identify the domain and range of the relation.. . {(-9, 2), (-4, 2), (3, 2), (9, 2)}
    5·2 answers
  • Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates (12,5) lies on
    9·1 answer
  • Calvin had $10. When he bought 7 colored pencils and 2 notebook at $1.30 per notebook, the change was $1.10 what is the price of
    8·2 answers
  • Identify the base of the parallelogram, given that A=81x2 cm2.
    11·2 answers
  • Explain your answer <br><br> Thank you so much ! <br><br> Will give brainlst
    13·1 answer
  • Help me pls helpppppppppppppppppppppppppp
    10·1 answer
  • 40 points
    15·1 answer
  • Help help help help help
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!