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Tju [1.3M]
3 years ago
13

How can exponential and logarithmic functions be combined?

Mathematics
1 answer:
OLEGan [10]3 years ago
4 0
It really depends on the question and what you want to solve. An exponential function can be written as y = x^2 and if you are solving for y then it will be log(base x) y = 2.

More Examples:
3x = 15
(log both sides with base of 3)
log(3)3x = log(3)15
since log(3)3 = 1 then,
(1)x = log(3)15
x = log 15 / log 3
= 2.465
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Is the solution of this equation extraneous?
UkoKoshka [18]

Answer:

x = - 3 is extraneous

Step-by-step explanation:

Given

\sqrt{x+7} - 1 = x  ( add 1 to both sides )

\sqrt{x+7} = x + 1 ( square both sides )

x + 7 = (x + 1)² ← distribute right side

x + 7 = x² + 2x + 1 ( subtract x + 7 from both sides )

0 = x² + x - 6 ← in standard form

0 = (x + 3)(x - 2) ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions.

x = - 3 : \sqrt{-3+7} - 1 = \sqrt{4} - 1 = 2 - 1 = 1 ≠ - 3

x = 2 : \sqrt{2+7} - 1  = \sqrt{9} - 1 = 3 - 1 = 2

x = 2 is a solution and x = - 3 is extraneous

6 0
3 years ago
Read 2 more answers
Given r(x) =11/(x-4)^2 which represents a domain restriction on r(x) and the corresponding inverse function?
saul85 [17]

Answer:x>4;r-1(x)=4-(root of (11/x))

Step-by-step explanation:

Edgenuity 2020

6 0
3 years ago
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If 400 g of chocolate sells for $12,<br> "how much is the cost per kilogram?
Kryger [21]

the cost of the chocolate of 1 kg will be 30$

4 0
3 years ago
Alden paid to have some programs printed for the football game last weekend. The printing cost per program was 54 cents, and the
uranmaximum [27]

Answer:

300 programs

Step-by-step explanation:

Let’s work with cents to make this easier. We convert the $12 to cents, making 1200 cents

Let the number of copies Alden printed be x. His total printing cost would be x * 54 = 54x cents.

He sold at 75 cents each and still had left 100 copies. This means his total sale would be (x - 100)75

He lost $12 on the venture. This means his cost price minus his selling price is $12 since it’s a loss.

Computing this:

54x - 75(x - 100) = 1200

54x - 75x + 7500 = 1200

-21x = 1200 - 7500

-21x = -6,300

x = 6300/21 = 300 programs

4 0
3 years ago
There were 6872 men and women at a concert. There were 2150 more men than women. How many men were there at the concert?​
eduard

Answer:

Men/ women=6872

women =2150

:6872-2150=4,722

4 0
3 years ago
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