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3 years ago

What is the true solution to the equation below?

Mathematics

1 answer:

jarptica [38.1K]3 years ago

3 0

Answer:

Step-by-step explanation:

some rules of logarithmic function

$ln(a) - ln(b)=ln(\frac{a}{b})$

$e^{ln(a)}=a$

$ln(a)^{n}=nln(a)$ vice-versa $nln(a)=ln(a)^{n}$

If ㏑(a) = ㏑(b), then a = b

∴ $2ln(e^{ln(2x)})-ln(e^{ln(10x)})=ln(30)$

Use the 2nd rule to simplify it

$e^{ln(2x)}=2x\\e^{ln(10x)}=10x\\$

2㏑(2x) - ㏑(10x) = ㏑(30)

Use the 3rd rule in the 1st term

∵ 2㏑(2x) = ㏑(2x)² = ㏑(4x²)

∴ ㏑(4x²) - ㏑(10x) = ㏑(30)

- Use the 1st rule with the left hand side

$ln(4x^{2})-ln(10x)=ln(\frac{4x^{2}}{10x})\\\\ln(\frac{4x^{2}}{10x})=ln(30)\\\\ \frac{4x^{2}}{10x}=\frac{2x}{5}=\frac{2}{5}x\\\\ ln(\frac{2}{5}x)=ln(30)$

Use the 4th rule

$\frac{2}{5} x = 30$

Multiply both sides by 5

∴ 2 x = 150

- Divide both sides by 2

∴ x = 75

The value of x = 75

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Joy recorded the distances she walked each day for five days. How far did she walk in 5 days? Line plot: 3 xs on 1/3 1 x on 1/2

kotykmax [81]

Answer:

$2\frac{1}{6}\approx 2.167$ units.

Step-by-step explanation:

We have been given that Joy recorded the distances she walked each day for five days.

To find the distance traveled be Joy in 5 days we will add the distances covered by Joy each day.

As there are 3 dots on 1/3, this means that Joy traveled 1/3 units on 3 days.

Since there is 1 dot on 1/2 and on dot on 2/3, so this means that Joy walked 1/2 units one day and 2/3 units another day.

Let us add all these distances.

$\text{Total distance walked by Joy in 3 days}=3\times\frac{1}{3}+\frac{1}{2}+\frac{2}{3}$

$\text{Total distance walked by Joy in 3 days}=\frac{1*3}{3}+\frac{1}{2}+\frac{2}{3}$

Let us have a common denominator.

$\text{Total distance walked by Joy in 3 days}=\frac{3*2}{3*2}+\frac{1*3}{2*3}+\frac{2*2}{3*2}$

$\text{Total distance walked by Joy in 3 days}=\frac{6}{6}+\frac{3}{6}+\frac{4}{6}$

$\text{Total distance walked by Joy in 3 days}=\frac{6+3+4}{6}$

$\text{Total distance walked by Joy in 3 days}=\frac{13}{6}$

$\text{Total distance walked by Joy in 3 days}=2\frac{1}{6}$

Therefore, Joy traveled $2\frac{1}{6}\approx 2.167$ units in 5 days.

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4 years ago

PLEASE AWNSEERRRRRRRRRRR wILL GIVE BRANILIEST

Marysya12 [62]

Answer:

Step-by-step explanation:

1=5-4+3-2-1;

2=(5-4+3-2)*1;

3=((5+4)/3) * (2-1);

4=(5+4-3-2)*1;

5=5*(4-3)*(2-1);

6=5-4+(3*2)-1;

7=5+4-3+2-1;

8=(5+4-3+2)*1;

9=5+4+3-2-1;

10=5+4+(3-2)*1;

11=5+4+3-2+1;

12=(5+4-3)*(2*1);

13=((5+4-3)*2)+1;

14=(5+4+3+2)*1;

15=5+4+3+2+1;

16=5+4+(3*2)+1;

17=5+(4*3)*(2-1);

18=5+(4*3)+2-1;

19=(5*4)-3+(2*1);

20=(5*4)-3+2+1;

21=(5*4)+3-(2*1);

22=(5*4)+3-2+1;

23=(5*4)+3*(2-1);

24=(5*4)+3+2-1;

25=(5*4)+3+(2*1);

26=(5*4)+3+2+1;

27=(5*4)+(3*2)+1;

28=5+(4*3*2)-1;

29=5+(4*3*2*1);

30=5+(4*3*2)+1;

31=((5*4*3)/2)+1;

32=5*(4+3)-2-1;

33=5*(4+3)-(2*1);

34=5*(4+3)-2+1;

35=5*(4+3)*(2-1);

36=5*(4+3)+2-1;

37=5*(4+3)+(2*1);

38=5*(4+3)+2+1;

(no equation for 39);

40=5*(4+3+2-1)

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2 years ago

Read 2 more answers

What's the area of the circle with the diameter of 8

dimaraw [331]

Step-by-step explanation:

General formula for the area of a circle = πr^2.

Since the diameter is 8, the radius is 4 (half of diameter)

So the area is π(4)^2 = 16π.

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3 years ago

5^(-7)*5^(12)*5^(-2)<br><br> with steps

docker41 [41]

Answer:

=125

Step-by-step explanation:

5−7)(512)(5−2)

78125

(512)(5−2)

78125

(512)(5−2)

78125

(244140625))(5−2)

=3125(5−2)

=3125(

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4 years ago

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An angle's supplement is nine times of its complementary angle. Find the measure of the angle, the complement of the angle,and t

Masja [62]

Answer:

Measure of required angle = 78.75° , measure of complementary angle = 11.25° and measure of supplementary angle = 101.25°

Step-by-step explanation:

let assume measure of required angle = x

since sum of angle and its supplement is 180°

so x + supplement of x = 180

⇒ supplement of x = 180 - x

since sum of angle and its complement is 90

so x + complement of x = 90

⇒ complement of x = 90 - x

Form given information

supplement of x = 9 × ( complement of x)

⇒180 - x = 9 × ( 90 - x )

⇒ 180 - x = 810 - 9x

⇒ -x + 9x = 810 - 180

⇒ 8x = 630

⇒ x = 630/8 = 78.75°

complement of x = 90 - x = 90 - 78.75° = 11.25°

and supplement of x = 180 - 78.75 = 101 .25°

we can recheck our solution by multiplying complement by 9 , that is 11.25 × 9 = 101.25 which is same as supplement. Hence our solution is correct.

So we can conclude that measure of required angle = 78.75° , measure of complementary angle = 11.25° and measure of supplementary angle = 101.25°

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3 years ago