Question

if a$if a^1\x=b^1\y=c^1\z and abc=1,prove that x+y+z=0$

Answer 1

Hello Friend,

Here's the answer.


The Identities used are:

• log ab = log a + log b
• n log a = log aⁿ
• log 1 = 0

Hope it helps.

Purva
@Purvaparmar1405
Brainly.in

Answer 2

Question :- if a^(1/x) = b^(1/y) = c^(1/z) , and abc = 1 , prove that, x + y + z = 0 .

Solution :-

Let us assume that,

→ a^(1/x) = b^(1/y) = c^(1/z) = k , (where k is a constant number.)

then,

→ a^(1/x) = k

→ a = k^x

similarly,

→ b^(1/y) = k

→ b = k^y

and,

→ c^(1/z) = k

→ c = k^z .

given that,

→ a * b * c = 1 .

putting above values we get,

→ k^x * k^y * k^z = 1

using a^l * a^m * a^n = a^(l + m + n) , we get,

→ k^(x + y + z) = 1

now, we know that, if power of a number is 0 , it is equal to 1,

therefore,

→ k^(x + y + z) = k^0

now, we know that, when base is same, powers are equal . { a^m = a^n => m = n }

hence,

→ (x + y + z) = 0 (Proved.)

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