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
bekas [8.4K]
2 years ago
8

Find the Domain of the following exponential and logarithmic equations and solve them:

Mathematics
1 answer:
kakasveta [241]2 years ago
5 0

The base of a logarithm should always be positive and can't be equal to 1, so the domain is 0 < <em>x</em> < 1 or <em>x</em> > 1.

\log_{\frac1x}243=5

Write both sides as powers of 1/<em>x</em> :

\left(\dfrac1x\right)^{\log_{\frac1x}243}=\left(\dfrac1x\right)^5

Recall that a^{\log_ab}=b, so that

243=\left(\dfrac1x\right)^5

243=\dfrac1{x^5}

x^5=\dfrac1{243}

Take the 5th root of both sides, recalling that 3⁵ = 243, so

x=\sqrt[5]{\dfrac1{243}}=\boxed{\dfrac13}

You might be interested in
A bag of Halloween M&amp;M’s contains 4 orange, 5 brown and 6 yellow candies. Two candies are selected without replacement. Let
Montano1993 [528]
P(A)= 4+5+6= 15/2= 75%
P(B)= 6+4=10  5/10= 50%
P(C)= 5+4=9    6/9= 66.6%

4 0
3 years ago
Required<br> What is the solution for the system below:<br> y = x + 1 and y = x + 1
Dmitry_Shevchenko [17]

Answer:

Y TO THE POWER 3 BY DIVIDING Y ON BOTH SIDES YOU WILL GET Y TO THE POWER 3

Step-by-step explanation:

3 0
2 years ago
30 points!
madreJ [45]
You would start at (0,36) and then move to (1, 24) , (2,12), (3,0) because he gives out 12 bags per hour 
7 0
2 years ago
Read 2 more answers
What is the length of segment AC?<br><br> (Picture attached)
natka813 [3]
6^2 + 8^2 = c^2. \newline&#10;36 + 64 = c^2. \newline&#10;c = \pm10 \Rightarrow AC = 10.
8 0
3 years ago
So if you went 24 laps, how many minutes would
Licemer1 [7]

Answer:

24 lap of?....

Step-by-step explanation:

probably 2 minz

4 0
3 years ago
Other questions:
  • Mandy has three stuffed animals. Two of the animals have a mass of 200 grams each, and the third one has a mass of 250 grams. Wh
    5·2 answers
  • Evaluate 2r(t+8) if r=3 and t=5
    12·1 answer
  • What is 6/54 equivalent to
    11·2 answers
  • Among all right triangles whose hypotenuse has a length of 12 cm, what is the largest possible perimeter?
    9·1 answer
  • -1 3/7 x (-3 2/3) <br> Thank you
    13·2 answers
  • If we recreated the scene from Fast &amp; Furious 7 and dropped a Challenger SRT® Hellcat Redeye Widebody from a C-130 aircraft
    14·2 answers
  • 4. Sam Howard's bank charges a $1.23
    13·1 answer
  • Justin, Cam, and Ben are playing a board game where exactly one player will win. Ben estimates that Justin has a 20\%20%20, perc
    12·1 answer
  • - If m <br> measures of the two angles.
    14·1 answer
  • The solution of a+b&gt;−4 is a&gt;−9. What is the value of b?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!