Multiplying a number by 4/5 then dividing by 2/5 is the same as multiplying by what number?

Answer:

[tex]\log _3\left(81\right)=4[/tex]

Step-by-step explanation:

Given : [tex]\log _3\left(81\right)[/tex]

We have to find the value of [tex]\log _3\left(81\right)[/tex]

Consider [tex]\log _3\left(81\right)[/tex]

Rewrite 81 in base power form, [tex]81=3^4[/tex]

[tex]=\log _3\left(3^4\right)[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]

We have,

[tex]\log _3\left(3^4\right)=4\log _3\left(3\right)[/tex]

[tex]=4\log _3\left(3\right)[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1[/tex]

[tex]\log _3\left(3\right)=1[/tex]

[tex]=4\log _3\left(3\right)=4[/tex]

Thus,  [tex]\log _3\left(81\right)=4[/tex]

4

Now, we will solve the problem of the logarithm.

Some logarithmic properties used this time are as follows:

[tex]\boxed{ \ \log_{a} a = 1 \ }[/tex]

[tex]\boxed{ \ \log_{a}b^c = c \log_a b \ }[/tex]

Let us calculate the value of [tex]\boxed{ \ \log_3 81 \ }[/tex]

Recall that [tex]\boxed{ \ 81 = 3^4. \ }[/tex]

[tex]\boxed{ \ \log_3 81 = \log_3 3^4 \ }[/tex]

[tex]\boxed{ \ \log_3 81 = 4 \log_3 3 \ }[/tex]

[tex]\boxed{ \ \log_3 81 = 4 \times 1 \ }[/tex]

Thus, the result is [tex]\boxed{\boxed{ \ \log_3 81 = 4 \ }}[/tex]

- - - - - - -

Alternative problem:

What is the value of [tex]\boxed{ \ \log_{81} 3 \ ? \ }[/tex]

Recall that [tex]\boxed{ \ 3 \rightarrow (3^4)^{\frac{1}{4}} \rightarrow 81^{\frac{1}{4}}. \ }[/tex]

[tex]\boxed{ \ \log_{81} 3 = \log_{81} 81^{\frac{1}{4}} \ }[/tex]

[tex]\boxed{ \ \log_{81} 3 = \frac{1}{4} \log_{81} 81 \ }[/tex]

[tex]\boxed{ \ \log_{81} 3 = \frac{1}{4} \times 1 \ }[/tex]

Thus, the result is [tex]\boxed{\boxed{ \ \log_{81} 3 = \frac{1}{4} \ }}[/tex]

- - - - - - -

Notes:

The relationship between logarithms and exponents is as follows:

[tex]\boxed{ \ \log_{a}b = c \ } \leftrightarrow \boxed{ \ a^c = b \ }[/tex]

Keywords: what is the value of log3 81, logarithmic properties, base, numerous, exponential functions, inverses each other

The total number of people that attended dan's birthday party is;

30 People

We are told that 5 classmates attended dan's birthday party.

Number of classmates at birthday party = 5

We are told that this 5 people is only half of his summer camp friends that attended the birthday party.

Thus, number of summer camp friends that attended = 5 × 2 = 10

Similarly the 5 people is only a third of his relatives that attended the birthday party.

Thus, number of relatives that attended = 5 × 3 = 15

Therefore,

total number of people that attended dan's birthday party = 5 + 10 + 15 = 30 people

Read more at; https://brainly.com/question/11242816

The expression is 8 + n.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

A phrase: “twice the sum of four and a number”.

Let the number is n.

The according to the question:

Twice the sum of the four = 8

And a number 8 + n.

Therefore, the expression is 8 + n.

To learn more about the expression;

brainly.com/question/24242989  

#SPJ6

Compound inequalities are used to group at least two inequalities

The open sentence that could result in the solution set is r<6 or r>4

From the question, we understand that the solution set consists of real numbers

From the list of options, only the open sentence r<6 or r>4 satisfy the given condition.

This is so because;

r<6 or r>4 = {4.0...... to 5.99...}

The solution set of other open sentence are not true

Hence, the open sentence that could result in the solution set is r<6 or r>4

Read more about compound inequalities at:

https://brainly.com/question/24544713

The image that represents the final image after the transformation is: Image 4

Given transformation rule is ry-axis ◦ T3, -1.

First of all, we will reflect the coordinates of LMNP across y axis by the rule: (x, y) -> (-x, y)

Then, we will carry out a translation of shifting 3 units to the right and then 1 unit down.

So, if the original point was (x, y), after the translation of it becomes (x + 3, y - 1 ).

Now, the coordinates of LMNP are:

L (-5, 1)

M (-5, 4)

N(-3, 4)

P(-3, 1).

Then, after reflection from y axis, we have:

L' (5, 1),

M' (5, 4),

N'(3, 4)

P'(3, 1).

Then, after Transformation T (3, -1) the coordinates are:

L' (5 + 3, 1 - 1)  - L"(8, 0),

M' (5 + 3, 4 - 1) = M"(8, 3),

N'(3+3, 4-1) = N"(6, 3),

P'(3+3, 1-1) = P"(6, 0)

Therefore, the required transformed figure is (4).

Read more about Coordinates after transformation at: https://brainly.com/question/4289712

#SPJ2

To find the values of x and y, we need to set up and solve a system of two equations based on the fact that the angles form a linear pair and are congruent.

You are asked to find the values of x and y in two congruent angles which are linear pairs. A linear pair is a set of adjacent angles whose uncommon sides form a straight line, thus their sum is 180 degrees. Therefore, we can form the equation (7x + 34)° + (2y/3)° = 180°.

Since the two angles are also congruent (meaning they have the same measure), we can also form the equation (7x + 34)° = (2y/3)°. Now you have a system of two equations that you can solve to find the values of x and y.

https://brainly.com/question/24583039

#SPJ11

We are given that about 56% of the 2,553 students are enrolled in at least one honors lass.

So we basically need to find the value of 56% of 2553

converting 56% to decimal we get 56/100 =0.56

now multiplying 0.56 with 2553, we get

0.56*2553=1429.68

Rounding off we get 1430

Answer : 1430 students are enrolled in an honors class

Answer:

Answer : 1430 students are enrolled in an honors class

Step-by-step explanation:

Answer:

Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.

Step-by-step explanation: