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3 years ago

Simplify into one logarithm 2 log x + 3 log y

1 answer:

const2013 [10]3 years ago

8 0

If a logarithm has a coefficient, then the coefficient can also be written as the exponent of the input of the logarithm. In other words, if you have the logarithm alog(x), that is equal to log(x^a). So the expression can be rewritten:

log(x^2)+log(y^3)

If tow logarithms of the same bases are added together that is equal to the logarithm of the product of the inputs of the two original logarithms. In other words, given log(x)+log(y), it can also be written as log(xy). So the expression can be combined into one logarithm:

log(x^2 * y^3)

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postnew [5]

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)).

Let the functions be f(x) = 4x² + 1 and g(x) = x² - 3

The correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

<h3>What is composition function?</h3>

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g exists used for the outcome of applying the function f to x.

Given:

f(x) = 4x² + 1 and g(x) = x² - 3

a) (f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

substitute the value of g(x) in the above equation, and we get

= 4(x⁴ - 24x + 9) + 1

simplifying the above equation

= 4x⁴ - 96x + 36 + 1

= 4x⁴ - 96x + 37

(f o g)(x) = 4x⁴ - 96x + 37

b) (g o f)(x) = g[f(x)]

substitute the value of g(x) in the above equation, and we get

g[f(x)] = (4x² + 1)²- 3

= 16x⁴ + 8x² + 1 - 3

simplifying the above equation

= 16x⁴ + 8x² - 2

(g o f)(x) = 16x⁴ + 8x² - 2.

Therefore, the correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

To learn more about the function refer to:

brainly.com/question/26709985

#SPJ9

7 0

2 years ago

A sphere with center A is shown. Which represents a tangent?<br> | WE

lana [24]

Answer:

<h2>The segment FE is a tangent of the sphere.</h2>

Step-by-step explanation:

Obseve the sphere in the image attached.

Notice that point A is the center of the sphere. GD is the diameter, which means AG and AD are radius.

On the other hand, remember that a tangent is a line that intersects the figure at only one point, otherwise, it would be a secant.

Therefore, segment BC is a secant and segment FE is tangent.

So, the right answer is segment FE.

4 0

3 years ago

Ken read 30 pages of a book on monday and 1/8 of the book on tuesday, he completed the remaining 1/4od the book on wednesday.how

dlinn [17]

Let the total amount of pages be t
t=30+1/8t+2/8t
now simplify
t=30+3/8t
5/8t=30
divide 30 by 5
1/8=6
now you know 1/8 of the book is 6 pages which means the whole book has 48 pages.

7 0

3 years ago

What do you notice about the angle measures?

Aleksandr-060686 [28]

1. Two angles are acute, while the other is square

2. They all add up to 180°

7 0

2 years ago

A square has a side of 5 ft. What is<br> the perimeter of the triangle?

luda_lava [24]

I'll draw it for you cause im nice.

Ok so if you have 5ft on a square, all the sides are 5ft.

That mean that if its in half, one of the sides will be 2.5ft.

Now you can add 2.5 + 2.5 + 5+5 = 15.

So its 15 ft.

8 0

3 years ago