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If Ax = B, by = C and Cz = A, Prove That: Xyz = 1. - Mathematics

Sum

If ax = b, by = c and cz = a, prove that : xyz = 1.

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Solution

We are given that
ax = b, by = c and cz = a
Consider the equation
ax = b
⇒ axyz = byz      [ raising to the power yz on both sides ] 
⇒  axyz = (by)z
⇒ axyz = c        [ ∵ by = c ]
⇒  axyz = cz
⇒  axyz = a         [ ∵ cz = a ]
⇒  axyz = a1
⇒  xyz = 1

Concept: Solving Exponential Equations
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (B) | Q 8 | Page 100
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