Math, asked by Deva6680, 1 year ago

If
a {}^{x}  = b \\ b {}^{y}  = c   \\ c {}^{z}  = a
then prove
x \times y \times z = 1

Answers

Answered by Anonymous
1
hope this helps you.......
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Mankuthemonkey01: yeah
Mankuthemonkey01: But you should have told him bcoz i guess he thought both are related
Mankuthemonkey01: I guess he didn't saw that bro
Mankuthemonkey01: chill bro
Mankuthemonkey01: u r brainliest
Deva6680: please explain in a better way
Deva6680: so i can understand
Answered by Mankuthemonkey01
0
Hey mate!!!!!

Given
 {a}^{x} = b
so we can write b^y as
( {a}^{x} ) {}^{y}
and also given that c^z is a
so we can write
 (({c}^{z} ) {}^{x} ) {}^{y}
By opening brackets we have

 {c}^{zxy}
now we know that
 {a}^{x} = b \\ {a}^{xy} = c

because b^y = a^xy = c

and also

 {a}^{xy} = {c}^{xyz}
so
 {a}^{xy} = {c}^{xyz} = c
because a ^xy = c

so
now bases are same and c = c^1

so

 {c}^{xyz} = {c}^{1}
now since bases are same we can write
xyz = 1

Hope it helps dear friend ☺️✌️✌️
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Deva6680: I could not understand can give this solution in easy way so I understand better
Mankuthemonkey01: Now it is not possible because editing will not show powers
Deva6680: can you do in rough copy and please send that solution
Mankuthemonkey01: wait
Deva6680: ok thank you for accepting my request
Mankuthemonkey01: welcome
Mankuthemonkey01: done check it
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