If 2^x=3^y=12^z then prove it 2/x = 1/z -1/y.​

1 answer
Question:

If 2^x=3^y=12^z then prove it 2/x = 1/z -1/y.​

Answers

SOLUTION:[tex] \begin{array}{l} 2^x = 3^y = 12^z \\ 2^x = 3^y = 2^{2z} \cdot 3^z \\ \Rightarrow 3 = 2^{\frac{x}{y}} \\ \Rightarrow 2^x = 2^{2z} \cdot 2^{\frac{xz}{y}} \\ \Rightarrow x = 2z + \frac{xz}{y} \\ \Rightarrow xy = 2zy + xz \\ \Rightarrow 2zy = xy - xz \\ \text{Dividing both sides by }xyz,\text{ we get:} \\ \dfrac{2}{x} = \dfrac{1}{z} - \dfrac{1}{y} \end{array} [/tex]

Similar Solved Questions

1 answer

PLEASE HELP!!! Will give BRAINLIEST!!

PLEASE HELP!!! Will give BRAINLIEST!!...
2 answers

What number is one tenth as much as 65

What number is one tenth as much as 65...
2 answers

Write the following phrase as an inequality: 3 more than twice n is at most 50.

Write the following phrase as an inequality: 3 more than twice n is at most 50....
1 answer

Please someone help !!!!​

please someone help !!!!​...
2 answers

What body parts or organs are used to digest food?

what body parts or organs are used to digest food?...
1 answer

How many solutions does 7(x - 2) + 5 = 3 (2x - 1) + 1 have?

How many solutions does 7(x - 2) + 5 = 3 (2x - 1) + 1 have?...
2 answers

Who tore my scarf ? is transitive or intransitive​

who tore my scarf ? is transitive or intransitive​...
2 answers

Order the side lengths

Order the side lengths...
1 answer

In the SI units, what makes the base units special

In the SI units, what makes the base units special...
1 answer

Question 1 : Can 2 Yards And 60 Inches Be Expressed as a ratio. If Yes, Express In Simplest Form . Question 2 : Can 3 Gallons And 5 Tons Be Expressed As A ratio. If Yes, Express In Simplest Form .

Question 1 : Can 2 Yards And 60 Inches Be Expressed as a ratio. If Yes, Express In Simplest Form . Question 2 : Can 3 Gallons And 5 Tons Be Expressed As A ratio. If Yes, Express In Simplest Form ....
1 answer

How did the yalta conference affect Germany and Europe after world war 2

How did the yalta conference affect Germany and Europe after world war 2...
1 answer

When economists speak of "demand" in a particular market, they refer to?

When economists speak of "demand" in a particular market, they refer to?...
1 answer

The principle of cross-cutting relationships states that certain features-

The principle of cross-cutting relationships states that certain features-...
2 answers

Find the slope and y-intercept of the line. 3x+4y=-7 write your answers in simplest form. slope : y - intercept : (spammers reported) will mark the brainliest.

Find the slope and y-intercept of the line. 3x+4y=-7 write your answers in simplest form. slope : y - intercept : (spammers reported) will mark the brainliest....
2 answers

Helppppppp!!! 2v+18=16-4 (v+7)

helppppppp!!! 2v+18=16-4 (v+7)...
2 answers

Of 56 people watching a soccer game, 21 are rooting for the away team. Which of the following is the fraction of people rooting for the away team"​

of 56 people watching a soccer game, 21 are rooting for the away team. Which of the following is the fraction of people rooting for the away team"​...
2 answers

What do the words partial,palatial and potential have in common

what do the words partial,palatial and potential have in common...
1 answer

How would this following triangle be classified

How would this following triangle be classified...
2 answers

Match the following items with their definitions. 1. capable of being dissolved in a liquid solvent 2. not capable of being dissolved in a liquid soluble 3. to break up in unit parts to form a solution dissolve 4. the substance that is dissolved in the solution solute 5. the substance that does the dissolving insoluble

Match the following items with their definitions. 1. capable of being dissolved in a liquid solvent 2. not capable of being dissolved in a liquid soluble 3. to break up in unit parts to form a solution dissolve 4. the substance that is dissolved in the solution solute 5. the substance that d...

-- 0.053133--