Question

if log x to the base y +log y to the base x =7 find (log x to the base y )^2+(log y to the base x)^2​

Answer 1

Hey Buddy

Here's The Answer

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I'm using ( a ) at place of ( y ), due to some technical issues in notations!

Given :

logₐ( x ) + logₓ( a ) = 7

To Find :logₐ( x )² + logₓ( a )²

We'll be using a property, log aᵇ = b × log a

Solution :

=> logₐ( x )² + logₓ( a )²

=> 2 × logₐ( x ) + 2 × logₓ( a )

Taking to as common

=> 2 [ logₐ( x )+ logₓ( a ) ]

Putting value of logₐ( x )+ logₓ( a ) , which is given.

=> 2 [ 7 ]=> 14

Hope It Helps.