Health High School

If 2^x=3^y=12^z, show that 1÷z=1÷y+2÷x.....​

Answers

Answer 1

Answer:

Proof of [tex]\dfrac{1}{z}}=\dfrac{1}{y}+\dfrac{2}{x}[/tex]  is shown below.

Explanation:

The given equation is

[tex]2^x=3^y=12^z[/tex]

To prove : [tex]\dfrac{1}{z}=\dfrac{1}{y}+\dfrac{2}{x}[/tex]

Proof : Let as assume,

[tex]2^x=3^y=12^z=k[/tex]

[tex]2^x=k\Rightarrow 2=k^{\frac{1}{x}}[/tex]    ...(1)

[tex]3^y=k\Rightarrow 3=k^{\frac{1}{y}}[/tex]      ...(2)

[tex]12^z=k\Rightarrow 12=k^{\frac{1}{z}}[/tex]    ...(3)

We know that

[tex]12=2\times 2\times 3[/tex]

[tex]12=(2)^2\times 3[/tex]

Using (1), (2) and (3), we get

[tex]k^{\frac{1}{z}}=(k^{\frac{1}{x}})^2\times k^{\frac{1}{y}}[/tex]

[tex]k^{\frac{1}{z}}=k^{\frac{2}{x}}\times k^{\frac{1}{y}}[/tex]

[tex]k^{\frac{1}{z}}=k^{\frac{2}{x}+\frac{1}{y}}[/tex]

On comparing both sides, we get

[tex]\dfrac{1}{z}}=\dfrac{2}{x}+\dfrac{1}{y}[/tex]

[tex]\dfrac{1}{z}}=\dfrac{1}{y}+\dfrac{2}{x}[/tex]

Hence proved.

Related Questions

List 3 examples of speech topics that would benefit from an emotional appeal focused on physical needs.

Answers

Answer:

Students answers will vary. Examples include: feeding the hungry, providing shelter for the homeless etc...answers should relate to people’s physical needs.

Explanation:

100% on edge

Students' answers will vary. Examples include: feeding the hungry, providing shelter for the homeless, etc.

What does emotional appeal mean?

Emotional appeal is a logical fallacy, whereby a debater tries to win a controversy by looking to get an emotional reaction from the opponent and target audience. it is usually characterized by the usage of loaded. language and ideas.

What is an emotional example?

Emotional appeals do not depend upon information or proof; alternatively, they depend upon gambling on emotions. Examples of appeal to Emotion: 1. Grocery shop industrial shows a happy circle of relatives sitting around the desk.

Learn more about Emotional appeals here: https://brainly.com/question/1837090

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A nursing instructor is teaching a session on the drugs used to treat benign prostatic hypertrophy. The instructor determines the session is successful when the students correctly choose which drugs that exert their effect by preventing testosterone conversion into an androgen?

Answers

Answer:

The correct answer is - Finasteride, Dutasteride

Explanation:

The treatment of benign prostatic hypertrophy by  Finasteride, Dutasteride helps in significant decrease in decrease in prostatic volume, obstruction and urinary flow increase in individual.

Dutasteride and finasteride  testosterone conversion into an androgen, and lower the quantity of a hormone known as dihydrotestosterone (DHT) responsible for growth of prostate.

Thus, the correct answer is - Finasteride, and Dutasteride.

Can you cure a virus? Can you cure a bacteria? Can you cure a fungus?

Answers

Answer: no i cant, no, and no

Answer:

There's no cure for it,But there's a treatment can help.

Explanation:

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