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3 years ago

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

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A store sells two different types of coffee beans; the more expensive one sells for $8 per pound, and the cheaper one sells for

Slav-nsk [51]

So,

Let the amount of the expensive coffee beans be x, and the amount of the less expensive coffee bean be y.

The number of pounds of coffee beans is 50.
x + y = 50

$8 times the amount of more expensive coffee beans plus $4 times the amount of less expensive coffee beans divided by 50 equals $6.50.
$\frac{8x + 4y}{50} = 6.50$

Now, all we have to do is use Elimination by Substitution.
x + y = 50

Subtract y from both sides.
x = 50 - y

Substitute 50 - y for x in the second equation.
$\frac{8(50 - y) + 4y}{50} = 6.50$

Distribute.
$\frac{400 - 8y + 4y}{50} = 6.50$

Collect Like Terms.
$\frac{400 -4y}{50} = 6.50$

Simplify.
$\frac{4(100 -y)}{2*5^2} = 6.50$
$\frac{2(100 -y)}{5^2} = 6.50$
$\frac{200 - 2y}{25} = 6.50$

Multiply both sides by 25.
$200 - 2y = 162.5$

Add 2y to both sides.
$200 = 162.5 + 2y$

Subtract 162.5 from both sides.
37.5 = 2y

Divide both sides by 2.
18.75 = y

Substitute in an earlier equation to solve for x.
x = 50 - y
x = 50 - 18.75
x = 31.25

Check.
31.25 + 18.75 = 50 lbs.

$\frac{8x + 4y}{50} = 6.50$
$\frac{8(31.25) + 4(18.75)}{50} = 6.50$
$\frac{250 + 75}{50} = 6.50$
$\frac{325}{50} = 6.50$
$\frac{5^2*13}{2 * 5^2} = 6.50$
$\frac{13}{2} = 6.50$
6.50 = 6.50 This also checks.

There were 31.75 pounds of the more expensive coffee bean and 18.75 pounds of the less expensive coffee bean.

8 0

3 years ago

Emma went out shopping with her father and bought a dress that cost $40.00. In class, she

dlinn [17]

Answer:

Both ways are correct

If you multiply the cost by 8% and add, you will still get 108% as your total.

7 0

3 years ago

Read 2 more answers

If the outside temperature is 15 Celsius,what is the temperature in degrees Fahrenheit? To express degrees Fahrenheit is degrees

olga55 [171]

Answer:

59 °F

Step-by-step explanation:

Put the given number in the formula and do the arithmetic.

F = (9/5)(15) +32 = 27 +32 = 59

The temperature in degrees Fahrenheit is 59.

4 0

3 years ago

Helppppppp pleaseeeee

ratelena [41]

Let's consider each of the options;

A) The range is the values that y can be of the function f(x). We can see that no matter what x values you put in, f(x)>0. It will never be negative. Although, if you put (1/2)^2, you can get a y value of (1/4) so this statement is incorrect.

B) It would have to put in the x or y value into the function and check. f(0)=(1/2)^0

You know that anything to the zero-th power gives 1, therefore, this statement is correct.

C) Again, if you put in a value such as (1/2)^2, you would be getting a number that is smaller than 1/2, so it isn't always increasing.

D) Again, it is possible to input any value in x and you would still be getting a positive y-value, therefore, this statement is incorrect.

Hope I helped :)

4 0

3 years ago

Use compatible numbers to estimate the quotient 315 divided by 8 answer quickly thank you!

lbvjy [14]

315 is about 320 which is divisible by 8 320/8 is 40

8 0

3 years ago

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