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
Fiesta28 [93]
3 years ago
11

expression to approximate log a of x for all positive numbers a, b, and x, where a is not equal to 1 and b is not equal to one

Mathematics
1 answer:
amid [387]3 years ago
7 0

Question:

Approximate log base b of x, log_b(x).

Of course x can't be negative, and b > 1.


Answer:

f(x) = (-1/x + 1) / (-1/b + 1)


Step-by-step explanation:

log(1) is zero for any base.

log is strictly increasing.

log_b(b) = 1

As x descends to zero, log(x) diverges to -infinity


Graph of f(x) = (-1/x + 1)/a is reminiscent of log(x), with f(1) = 0.


Find a such that f(b) = 1

1 = f(b) = (-1/b + 1)/a

a = (-1/b + 1)


Substitute for a:

f(x) = (-1/x + 1) / (-1/b + 1)

f(1) = 0

f(b) = (-1/b + 1) / (-1/b + 1) = 1




You might be interested in
A store is having a 20%-off sale on all merchandise. If Mai buys one item and saves $13, what was the original price of her purc
grin007 [14]

Answer:

The original price of her purchase was $65.

Step-by-step explanation:

From the information given, you know that $13 represents 20% of the original price and you can use a rule of three to find the value that represents 100%, which would be the original pice of her purchase:

$13 →  20%

 x   ← 100%

x=(13*100)/20

x=1300/20

x=65

According to this, the answer is that the original price of her purchase was $65.

8 0
2 years ago
Find the missing dimensions: Use the scale factor 1/4:3
katrin [286]

Answer:

The answer is 1/4!

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
If 64 feet of rope weighs 20 pounds how much will 80 feet of the same rope weigh
Nikolay [14]
It would weigh 25 pounds
6 0
3 years ago
Read 2 more answers
If y is 5 when x is 2.5 and y varies directly with x, find y when x is 10
ikadub [295]

Answer:

If x varies directly as y, then x=ky. y=5 and x=2.5 are substituted into x=ky to find k.

2.5=5k

k=2.5/5

k=5.

K =5 is substituted in x=ky to find y where x is 10.

x=5y

10=5y

y=10/2

y=2

8 0
3 years ago
Read 2 more answers
Factor the following polynomial.<br> 98x3 – 18x
grigory [225]

Answer:

2x(7x - 3)(7x +3)

Step-by-step explanation:

Find common factors between the 2 numbers:

98x^3 - 18x

2x(49x^2 - 9)

now find what numbers multiplied together is 49, and find what numbers added together equals 0 and the product is 3, 7 times 7 is 49 and 3(-3) = 9 while 3 - 3 = 0 so:

2x(7x - 3)(7x +3)

3 0
2 years ago
Read 2 more answers
Other questions:
  • A dog pen in the shape of a rectangle is to be built using one wall of a house as a side. If 132 feet
    11·1 answer
  • What is 7 to the 2nd power multiplied by 7 to the 3rd power
    7·2 answers
  • HURRY PLEASE!! How many sides are there in a regular polygon which has 120 degrees in each of its angeles?
    7·2 answers
  • What best describes the expression y over 3?
    14·1 answer
  • Find the length of LM:<br> K<br> 16<br> L<br> M
    6·1 answer
  • Does anybody know what 8(11-3) -2(4+1) is
    6·2 answers
  • Use the relationship between the angles in the figure to answer the question. which equation can be used to find the value of X?
    7·1 answer
  • Please help me (please dont send links)
    12·1 answer
  • Out of 4,000 colleges surveyed, 60% reported that SAT scores were not used as a high consideration in viewing their applications
    12·1 answer
  • I don’t know what to do here. If someone help me would be great!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!