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
fredd [130]
2 years ago
11

A teacher used the change of base formula to determine whether the equation below is correct.

Mathematics
2 answers:
Mademuasel [1]2 years ago
6 0

Answer:

The equation is correct

Step-by-step explanation:

The equation, written as:

[log_2 (10)][log_4 (8)][log_10 (4)] = 3

Consider the change of base formula:

log_a (x) = [log_10 (x)]/ [log_10 (a)]

Applying the change of base formula to change the expressions in base 2 and base 4 to base 10.

(1)

log_2 (10) = [log_10 (10)]/[log_10 (2)]

= 1/[log_10 (2)]

(Because log_10 (10) = 1)

(2)

log_4 (8)  = [log_10 (8)]/[log_10 (4)]

Now putting the values of these new logs in base 10 into the left-hand side of original equation to verify if we have 3, we have:

[log_10 (2)][log_8 (4)][log_10 (4)]

= [1/ log_10 (2)][log_10 (8) / log_10 (4)][log_10 (4)]

= [1/log_10 (2)] [log_10 (8)]

= [log_10 (8)]/[log_10 (2)]

= [log_10 (2³)]/[log_10 (2)]

Since log_b (a^x) = xlog_b (a)

= 3[log_10 (2)]/[log_10 (2)]

= 3 as required

Therefore, the left hand side of the equation is equal to the right hand side of the equation.

Amiraneli [1.4K]2 years ago
5 0

Answer:

B on E2020.

Step-by-step explanation:

You might be interested in
Two numbers whose sum is 44 and whose product is a maximum
Mashcka [7]

Answer:

x = y = 22

Step-by-step explanation:

It would help to know your math course. Do you know any calculus? I'll assume not.

Equations

x + y = 44

Max = xy

Solution

y = 44 - x

Max = x (44 - x)                    Remove the brackets

Max = 44x - x^2                   Use the distributive property to take out - 1 on the right.

Max = - (x^2 - 44x )               Complete the square inside the brackets.

Max = - (x^2 - 44x + (44/2)^2 ) + (44 / 2)^2 . You have to understand this step. What you have done  is taken 1/2 the x term and squared it. You are trying to complete the square. You must compensate by adding that amount on the end of the equation. You add because of that minus sign outside the brackets. The number inside will be minus when the brackets are removed.

Max = -(x - 22)^2 + 484

The maximum occurs when x = 22. That's because - (x - 22) becomes 0.

If it is not zero it will be minus and that will subtract from 484

x + y = 44

xy = 484

When you solve this, you find that x = y = 22 If you need more detail, let me know.


4 0
2 years ago
This is pretty simple, but the wording gets me. Is choice B correct as well, I’m not really sure. Please help
Oliga [24]
I’m not 100% sure but i think ur answer rn is correct don’t check the second box
7 0
2 years ago
A local pizzeria offers 14 toppings for their pizzas and you can choose any 5 of them for one fixed price. How many different ty
Ne4ueva [31]
C(14,5)=\dfrac{14!}{5!9!}=\dfrac{10\cdot11\cdot12\cdot13\cdot14}{2\cdot3\cdot4\cdot5}=2002
6 0
3 years ago
Plzzzzzzzzzzz Help me
Sati [7]

-3 < 0  Because -3 is less than 0.

Hope this helps ;P

3 0
3 years ago
Read 2 more answers
WILL MARK BRAINLIEST
Levart [38]

Answer:

There ya go

Step-by-step explanation:

3 0
2 years ago
Other questions:
  • 1 2 3 4 5 6 7 8 9 10
    15·1 answer
  • Crystal completed 1/3 of her homework assignment on Friday and 3/7 of her assignment on Saturday. what is the amount of her assi
    12·1 answer
  • An electrician charges an hourly rate of $50, but also charges a fixed fee for making house calls regardless of time spend on th
    15·1 answer
  • There are 5 cyclists in a race. There will be a first-place, a second-place, and a third-place prize awarded. In how many differ
    11·1 answer
  • Answer the word problem for 10 points​
    7·2 answers
  • Find the center and radius of the circle that has(-2,5)and(-4,9)as endpoints of the diameter.
    12·1 answer
  • Can someone help me with this I just need the equation.
    11·1 answer
  • Check the Screenshot
    9·2 answers
  • Find the repayment $5000 loaned for 4 years at 6% interest p.a What is the total amount What will be the monthly repayments?
    8·1 answer
  • 2. How many ounces of yeast will you need to make 30 rolls?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!