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
rosijanka [135]
3 years ago
5

Remember to show work and explain. Use the math font.

Mathematics
1 answer:
MrMuchimi3 years ago
6 0

Answer:

\large\boxed{1.\ f^{-1}(x)=4\log(x\sqrt[4]2)}\\\\\boxed{2.\ f^{-1}(x)=\log(x^5+5)}\\\\\boxed{3.\ f^{-1}(x)=\sqrt{4^{x-1}}}

Step-by-step explanation:

\log_ab=c\iff a^c=b\\\\n\log_ab=\log_ab^n\\\\a^{\log_ab}=b\\\\\log_aa^n=n\\\\\log_{10}a=\log a\\=============================

1.\\y=\left(\dfrac{5^x}{2}\right)^\frac{1}{4}\\\\\text{Exchange x and y. Solve for y:}\\\\\left(\dfrac{5^y}{2}\right)^\frac{1}{4}=x\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\dfrac{(5^y)^\frac{1}{4}}{2^\frac{1}{4}}=x\qquad\text{multiply both sides by }\ 2^\frac{1}{4}\\\\\left(5^y\right)^\frac{1}{4}=2^\frac{1}{4}x\qquad\text{use}\ (a^n)^m=a^{nm}\\\\5^{\frac{1}{4}y}=2^\frac{1}{4}x\qquad\log_5\ \text{of both sides}

\log_55^{\frac{1}{4}y}=\log_5\left(2^\frac{1}{4}x\right)\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\\dfrac{1}{4}y=\log(x\sqrt[4]2)\qquad\text{multiply both sides by 4}\\\\y=4\log(x\sqrt[4]2)

--------------------------\\2.\\y=(10^x-5)^\frac{1}{5}\\\\\text{Exchange x and y. Solve for y:}\\\\(10^y-5)^\frac{1}{5}=x\qquad\text{5 power of both sides}\\\\\bigg[(10^y-5)^\frac{1}{5}\bigg]^5=x^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(10^y-5)^{\frac{1}{5}\cdot5}=x^5\\\\10^y-5=x^5\qquad\text{add 5 to both sides}\\\\10^y=x^5+5\qquad\log\ \text{of both sides}\\\\\log10^y=\log(x^5+5)\Rightarrow y=\log(x^5+5)

--------------------------\\3.\\y=\log_4(4x^2)\\\\\text{Exchange x and y. Solve for y:}\\\\\log_4(4y^2)=x\Rightarrow4^{\log_4(4y^2)}=4^x\\\\4y^2=4^x\qquad\text{divide both sides by 4}\\\\y^2=\dfrac{4^x}{4}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\y^2=4^{x-1}\Rightarrow y=\sqrt{4^{x-1}}

You might be interested in
Eric and Stephanie took their younger sister Melissa to pick apples. Eric picked 4 times as many apples as
vodka [1.7K]

Answer:

Melissa picked 16 apples

Step-by-step explanation:

(Eric and Stephanie) 160 divided by 10 (I put ten because I add 6 and 4)

Which will equal 16.

Hope this helps ~~~~ :)

4 0
3 years ago
Read 2 more answers
Please help!! 40 points x
Alika [10]

Answer: x = 7

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What is the underlined sentence mean can someone explain
suter [353]

Step-by-step explanation:

1235

Now when we talk about place values we have ones tens hundreds thousands ten thousands and so on. So when you look at no.1 its place value is ones because 1 is the first value.

So 2 is in tens.

Now the difference of tens and hundreds is tens follows the 2 place value and hundreds the next.

HOPE ITS HELPFUL

8 0
2 years ago
Read 2 more answers
Find the equation of the linear function h that has h(12)=-7 and that is perpendicular to q(a)=1/2a+38.. I don’t understand how
Effectus [21]

Step-by-step explanation:

q(a) = ½a + 38

The slope of q is ½.  So the perpendicular slope is -1/½ = -2.

Write h(x) in point-slope form:

h − (-7) = -2 (x − 12)

h + 7 = -2 (x − 12)

Simplify to get slope-intercept form.

h + 7 = -2x + 24

h = -2x + 17

7 0
3 years ago
Ocean Bike Tours wants to provide bandanas for each person. The cost of the bandanas is each person. The cost of the bandana is
mixas84 [53]

Answer:

$145.50

Step-by-step explanation:

C = 45.50 + 2n

45.50 + 2X 100 = $145.50

7 0
3 years ago
Other questions:
  • Which is equivalent to a 270° clockwise
    14·1 answer
  • PLEASE ..... HELP THANK YOU
    11·2 answers
  • Find the area of the figure.(Sides meet at right angles)
    13·1 answer
  • What is the apparent solution to the system of equations? y=1/2x+2 y=2x−1
    5·1 answer
  • What is the slope of the line below? If necessary, enter your answer as a
    12·2 answers
  • What fraction and decimal in hundredths, is equivelant to 7/10
    14·1 answer
  • How much sit-ups can you do in 1 minutes?​
    8·1 answer
  • A triangle with 7,?, and form a right triangle.
    9·1 answer
  • If you were 2 years old in 2011 how old would you be in 2020?
    15·2 answers
  • Two processes in a manufacturing line are performed manually: operation A and operation B. A random sample of 50 different assem
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!