If a= 10^x, b = 10^y and a^yb^x = 100, show that: xy = 1 | Indices | SciPiPupil

Question: If $a=10^x, b=10^y, and a^yb^x = 100$, prove that: $xy = 1$.

Solution:

Given,

$a=10^x, b=10^y, and a^yb^x = 100$

To prove: $xy = 1$

We have,

$a^yb^x = 100$

$or, (10^x)^y × (10^y)^x = 10^2$

$or, 10^{xy} × 10^{xy} = 10^2$

$or, 10^{xy+xy} = 10^2$

$or, 2xy = 2$

$\therefore xy = 1$

#proved

Related Notes and Solutions:

Here is the website link to the notes of Indices.

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