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3 years ago

Which is 2logx - 6 log(x-9) written as a single logarithm.

Mathematics

2 answers:

Anton [14]3 years ago

5 0

Answer: option c

Step-by-step explanation:

To solve this problem you must keep on mind the properties of logarithms:

$log(b)-log(a)=log(\frac{b}{a})\\\\log(b)+log(a)=log(ba)\\\\a*log(b)=log(b)^a$

Therefore, knowing the properties, you can write the expression gven in the problem as shown below:

$2logx-6log(x-9)\\logx^2-log(x-9)^6\\\\log\frac{x^2}{(x-9)^6}$

Varvara68 [4.7K]3 years ago

5 0

Answer:

c edge

Step-by-step explanation:

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Find the zeros (roots) of the following equations. f(x) = 2x5 - 9x4 + 12x3 - 12x2 + 10x - 3 = 0

Talja [164]

Hi,
$f(1)=2*1^5-9*1^4+12*1^3-12*1^2+10*1-3\\
=2-9+12-12+10-3\\
=0\\

f(x)=(x-1)(2x^4-7x^3+5x^2-7x+3)\\


g(x)=2x^4-7x^3+5x^2-7x+3\\

g(3)=2*3^4-7*3^3+5*3^2-7*3+3\\
=162-189+45-21+3\\
=0\\

g(x)=(x-3)(2x^3-x^2+2x-1)\\

h(x)=2x^3-x^2+2x-1\\

h( \dfrac{1}{2} )=2* \dfrac{1}{8} - \dfrac{1} {4}+1-1\\
=0\\

h(x)=(2x-1)(x^2+1)\\


f(x)=(x-1)(x-3)(2x-1)(x+i)(x-i)\\


$
Roots are 1,3,0.5,i,-i.

8 0

3 years ago

Use the graph below to write the equation of the function

Ksivusya [100]

Answer:

Step-by-step explanation:

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8 0

3 years ago

My questions are in the picture please help

Marrrta [24]

21.

So to solve for the value of a variable in an equation, you would need to isolate x on one side. The first thing you have to do is multiply 2 and (x + 7) together, which can be rewritten as 2(x) + 2(7). After multiplying, your equation would be: $2x+14+3x=12$ , or A.

22.

So the rule with multiplying exponents with the same base is to add the exponents together, and the rule with dividing exponents with the same base is to subtract the exponents. Your equation will be simplified as such:

$4^{(3+4)-9}\\ 4^{7-9}\\ 4^{-2}$

Now the rule with converting negative exponents into fractions is $x^{-m}=\frac{1}{x^m}$ . In this case, 4^-2 would turn into $\frac{1}{4^2}$ , or C, which is your final answer.

6 0

3 years ago

Consider the vector x: x <- c(2, 43, 27, 96, 18) Match the following outputs to the function which produces that output. Opti

Nookie1986 [14]

Completed Question

Outputs to be matched to the functions are:

1,2,3,4,5
1,5,3,2,4
1, 4, 3, 5, 2
2, 18, 27, 43, 96

Answer:

sort(x): 2, 18, 27, 43, 96
order(x): 1, 5, 3, 2, 4
rank(x) : 1, 4, 3, 5, 2
none of these : 1, 2, 3, 4, 5

Step-by-step explanation:

Given the vector x: x <- c(2, 43, 27, 96, 18)

Sort

In R, the sort(x) function is used to arrange the entries in ascending or descending order. By default, R will sort the vector in ascending order.

Therefore, the output that matches the sort function is:

sort(x): 2, 18, 27, 43, 96

Rank

The rank function returns a vector with the "rank" of each value.

x <- c(2, 43, 27, 96, 18)

2 has a rank of 1
43 has a rank of 4
27 has a rank of 3
96 has a rank of 5
18 has a rank of 2

Therefore, the output of rank(x) is: 1, 4, 3, 5, 2

Order

When the function is sorted, the order function gives the previous location of each of the element of the vector.

Using the sort(x) function, we obtain: 2, 18, 27, 43, 96

In the vector: x <- c(2, 43, 27, 96, 18)

2 was in the 1st position
18 was in the 5th position
27 was in the 3rd position
43 was in the 2nd position
96 was in the 4th position

Therefore, the output of order(x) is: 1, 5, 3, 2, 4

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3 years ago

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irinina [24]

Answer:

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Step-by-step explanation:

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