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irga5000 [103]
3 years ago
6

Is it linear or exponential?? Will mark as brainliest if correct!​

Mathematics
1 answer:
Dovator [93]3 years ago
5 0

Answer:

linear

Step-by-step explanation:

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If 2 to the power x is equal to 3 Y is equal to 6 to the power z then prove that 1 by X + 1 by Y is equal to 1 by Z
Sladkaya [172]

If 2^{X}=3^{Y}=6^{Z} then \frac{1}{X}+\frac{1}{Y} is equal to \frac{1}{Z}

What is an exponent?

⇒An exponent refers to the number of times a number is multiplied by itself.

Multiplication of exponents

⇒ It is also known as the law on indices. For multiplication with the same base, we add the powers.

For the same base  a^{m} \times a^{n}=a^{m+n}

For the different base and same power  a^{m} \times b^{m} = (a\times b)^{m}

Calculation:

⇒ We have been given that 2^{X}=3^{Y}=6^{Z} and by this relation, we have to prove that: \frac{1}{X}+\frac{1}{Y}= \frac{1}{Y}

⇒ 2^{X}=3^{Y}=6^{Z}

2^{X}=6^{Z}

(2)^{X}=(2 \times3)^{Z}

2^{X}=3^{Z}\times 2^{Z}

By taking power of Y both sides

⇒ (2^{X})^{Y} =(2^{Z})^{Y} \times(3^{Z})^{Y}

(2^{X})^{Y} =(2^{Z})^{Y} \times(3^{Y})^{Z}

(2^{X})^{Y} =(2^{Z})^{Y} \times(2^{X})^{Z}

2^{XY}  =2^Z^Y \times2^X^Z

XY=ZY+XZ

On dividing by 1/XYZ into both sides we will get

⇒ \frac{1}{Z}=\frac{1}{X}+\frac{1}{Y}

Hence, it is now proved that if 2^{X}=3^{Y}=6^{Z} then\frac{1}{X}+\frac{1}{Y} is equal to \frac{1}{Z}

Learn more about the law of indices here :

brainly.com/question/170984

#SPJ9

3 0
2 years ago
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