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slamgirl [31]
3 years ago
12

Let f(x) = log(x). Find values of a such that f(kaa) = kf(a).

Mathematics
1 answer:
meriva3 years ago
3 0

Answer:

a = k^{\frac{1}{k-2}}

Step-by-step explanation:

Given:

f(x) = log(x)

and,

f(kaa) = kf(a)

now applying the given function, we get

⇒ log(kaa) = k × log(a)

or

⇒ log(ka²) = k × log(a)

Now, we know the property of the log function that

log(AB) = log(A) + log(B)

and,

log(Aᵇ) = b × log(A)

Thus,

⇒ log(k) + log(a²) = k × log(a)         (using log(AB) = log(A) + log(B) )

or

⇒ log(k) + 2log(a) = k × log(a)            (using log(Aᵇ) = b × log(A) )

or

⇒ k × log(a) - 2log(a) = log(k)

or

⇒ log(a) × (k - 2) = log(k)

or

⇒ log(a) = (k - 2)⁻¹ × log(k)

or

⇒ log(a) = \log(k^{\frac{1}{k-2}})          (using log(Aᵇ) = b × log(A) )

taking anti-log both sides

⇒ a = k^{\frac{1}{k-2}}

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Step-by-step explanation:

4 0
3 years ago
Paula finished the race at 2:14 p.m Beatrice finished the race 22 minutes earlier what time did Beatrice finish the race a 1:54
Digiron [165]

Answer: 1:52 PM

Step-by-step explanation:

PAULA: 2:14PM FINISHED THE RACE

BEATRICE: FINISHED 22 MINUTES EARLIER THEN PAULA

YOU TAKE 2:14PM AND SUBTRACT THE 22 MINS BEATRICE RAN TO GET YOU ANSWER.

SO 2:14 -14 MINS=2:00PM 14+8=22 (THE MINS BETRICE FINISHED)

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5 0
2 years ago
Can 8x be added to 56? Why or why not?<br> Use rich text?
Vladimir [108]

Answer:

see below

Step-by-step explanation:

8x and 56 are not like terms

x is a variable and 56 is a constant

8x can be added to 56 but they cannot be combined together into one term

8x+56 cannot be combined because they are not like terms

7 0
3 years ago
he Garcia family bought 400 yards of fencing to enclose a circular wildflower garden. They will use all of the fencing. a. What
frez [133]

9514 1404 393

Answer:

  • 127.32 yards diameter
  • 12,732.4 square yards area

Step-by-step explanation:

The diameter can be found from the circumference using the relation ...

  C = πd

  d = C/π = (400 yd)/π ≈ 127.32 yd . . . . diameter

The area is ...

  A = πr²

where the radius (r) is half the diameter.

  A = π(63.662 yd)² ≈ 12,732.4 yd² . . . . area

_____

<em>Additional comment</em>

We have used a full-precision value for pi. If you use 3.14, your answers will be different. Your diameter will be about 127.4 yards; your area about 12,738.9 yd².

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3 years ago
Na operação 6 (6-2+1) é usada qual propriedade?​
Dmitry [639]
30 is your answer

Hope it helps you
3 0
3 years ago
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