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3 years ago

Express 3^2 = x as a logarithmic equation.

1 answer:

8 0

Taking the log of both sides of the equation, you have
$2\log(3)=\log(x)$
Dividing by log(3), this looks like the change of base formula.
$\log_a(b)=\dfrac{\log(b)}{\log(a)}$

That is, division by log(3) gives
$2=\dfrac{\log(x)}{\log(3)}\\\\2=log_3(x)$

This apparently matches your first choice:
log3(x) = 2

You might be interested in

g 7. Find Re f and Im f and find their values at the given z. (Both answers should be included) f = z⁄(z + 1), z = 4 − 5

Schach [20]

Answer:

The real and imaginary parts of the result are $\frac{1441}{1601}$ and $\frac{4}{1601}$ , respectively.

Step-by-step explanation:

Let be $f(z) = \frac{z}{z+1}$ , the following expression is expanded by algebraic means:

$f(z) = \frac{z\cdot (z-1)}{(z+1)\cdot (z-1)}$

$f(z) = \frac{z^{2}-z}{z^{2}-1}$

$f(z) = \frac{z^{2}}{z^{2}-1}-\frac{z}{z^{2}-1}$

If $z = 4 - i5$ , then:

$z^{2} = (4-i5)\cdot (4-i5)$

$z^{2} = 16-i20-i20-(-1)\cdot (25)$

$z^{2} = 41 - i40$

Then, the variable is substituted in the equation and simplified:

$f(z) = \frac{41-i40}{41-i39} -\frac{4-i5}{41-i39}$

$f(z) = \frac{37-i35}{41-i39}$

$f(z) = \frac{(37-i35)\cdot (41+i39)}{(41-i39)\cdot (41+i39)}$

$f(z) = \frac{1517-i1435+i1443+1365}{3202}$

$f(z) = \frac{2882+i8}{3202}$

$f(z) = \frac{1441}{1601} + i\frac{4}{1601}$

The real and imaginary parts of the result are $\frac{1441}{1601}$ and $\frac{4}{1601}$ , respectively.

8 0

3 years ago

What is the algorithm for the inverse of f (x)?<br>

Juli2301 [7.4K]

Answer:

What is an inverse?

Recall that a number multiplied by its inverse equals 1. From basic arithmetic we know that:

The inverse of a number A is 1/A since A * 1/A = 1 (e.g. the inverse of 5 is 1/5)

All real numbers other than 0 have an inverse

Multiplying a number by the inverse of A is equivalent to dividing by A (e.g. 10/5 is the same as 10* 1/5)

What is a modular inverse?

In modular arithmetic we do not have a division operation. However, we do have modular inverses.

The modular inverse of A (mod C) is A^-1

(A * A^-1) ≡ 1 (mod C) or equivalently (A * A^-1) mod C = 1

Only the numbers coprime to C (numbers that share no prime factors with C) have a modular inverse (mod C)

Step-by-step explanation:

Please check image.

3 0

4 years ago

The Biology Club has 45 members, 35 girls and 10 boys. What is the ratio of

nignag [31]

Answer is A because as you se they have 45 members, 35 girls and 10 boys and you remember because i done it before

6 0

3 years ago

Read 2 more answers

A horse had 4 15 scoops of oats in his bucket. He ate 2 1/2 scoops of oats. How many scoops of oats are left in his bucket ?

Lunna [17]

2 1/2 because if u take away 4 from 2 u get 2 and a half left

6 0

4 years ago

This set of ordered pairs shows a relationship between x and y. {(0, -2), (3, 7), (6, 16), (6, 15), (8, 21), (10, 28), (11,31)}

Hunter-Best [27]

Answer:

The closest to the output when the input is approximately 12

Step-by-step explanation:

The given (x, y) coordinates are;

The line of best fit is

x, 0, 3, 6, 6, 8, 10, 11

y, -2, 7, 16, 15, 21, 28, 31

The line of best fit can be obtained from the scatter plot of the given data from where a linear pattern is apparent

A linear line of best fit is a trend line that gives an overall cumulative minimum distance of all the points from the line

The method for constructing a line of best fit includes;

1) The least Squares Method

2) The method of linear regression

3) Construction of line of best fit

a) The area method

b) The dividing method

The least squares equation is given as follows;

$\hat y$ = a + b·x

$b = \dfrac{\Sigma (x_i - \overline x) \cdot (y_i - \overline y)}{\Sigma (x_i - \overline x)^2 }$

From MS Excel, we have;

${\Sigma (x_i - \overline x) \cdot (y_i - \overline y)}{ }$ = 266.8571

${\Sigma (x_i - \overline x)^2 }$ = 89.42857

∴ b = 266.8571/89.42857 ≈ 2.984

$a =\overline y- b \cdot \overline x$

From MS Excel, with the given data, we get;

$\overline y$ = 16.57143

$\overline x$ = 6.285714

Therefore;

a = 16.57143 - 2.984 × 6.285714 = -2.185

Therefore, we get the following regression equation;

$\hat y$ = -2.185 + 2.9·x

Where;

x = The input

$\hat y$ = The output

Therefore, when x = 5, we get;

$\hat y$ = -2.185 + 2.9 × 5 = 12.315

Therefore, the closest to the output when the input is 5, y ≈ 12

8 0

3 years ago